Graphs, Surfaces and Homology

An Introduction to Algebraic Topology

Author: P. Giblin

Publisher: Springer Science & Business Media

ISBN: 9400959532

Category: Science

Page: 329

View: 500

viii homology groups. A weaker result, sufficient nevertheless for our purposes, is proved in Chapter 5, where the reader will also find some discussion of the need for a more powerful in variance theorem and a summary of the proof of such a theorem. Secondly the emphasis in this book is on low-dimensional examples the graphs and surfaces of the title since it is there that geometrical intuition has its roots. The goal of the book is the investigation in Chapter 9 of the properties of graphs in surfaces; some of the problems studied there are mentioned briefly in the Introduction, which contains an in formal survey of the material of the book. Many of the results of Chapter 9 do indeed generalize to higher dimensions (and the general machinery of simplicial homology theory is avai1able from earlier chapters) but I have confined myself to one example, namely the theorem that non-orientable closed surfaces do not embed in three-dimensional space. One of the principal results of Chapter 9, a version of Lefschetz duality, certainly generalizes, but for an effective presentation such a gener- ization needs cohomology theory. Apart from a brief mention in connexion with Kirchhoff's laws for an electrical network I do not use any cohomology here. Thirdly there are a number of digressions, whose purpose is rather to illuminate the central argument from a slight dis tance, than to contribute materially to its exposition.

Basic Concepts of Algebraic Topology

Author: F.H. Croom

Publisher: Springer Science & Business Media

ISBN: 1468494759

Category: Mathematics

Page: 180

View: 3902

This text is intended as a one semester introduction to algebraic topology at the undergraduate and beginning graduate levels. Basically, it covers simplicial homology theory, the fundamental group, covering spaces, the higher homotopy groups and introductory singular homology theory. The text follows a broad historical outline and uses the proofs of the discoverers of the important theorems when this is consistent with the elementary level of the course. This method of presentation is intended to reduce the abstract nature of algebraic topology to a level that is palatable for the beginning student and to provide motivation and cohesion that are often lacking in abstact treatments. The text emphasizes the geometric approach to algebraic topology and attempts to show the importance of topological concepts by applying them to problems of geometry and analysis. The prerequisites for this course are calculus at the sophomore level, a one semester introduction to the theory of groups, a one semester introduc tion to point-set topology and some familiarity with vector spaces. Outlines of the prerequisite material can be found in the appendices at the end of the text. It is suggested that the reader not spend time initially working on the appendices, but rather that he read from the beginning of the text, referring to the appendices as his memory needs refreshing. The text is designed for use by college juniors of normal intelligence and does not require "mathematical maturity" beyond the junior level.

Topology of Surfaces

Author: L.Christine Kinsey

Publisher: Springer Science & Business Media

ISBN: 1461208998

Category: Mathematics

Page: 281

View: 777

" . . . that famous pedagogical method whereby one begins with the general and proceeds to the particular only after the student is too confused to understand even that anymore. " Michael Spivak This text was written as an antidote to topology courses such as Spivak It is meant to provide the student with an experience in geomet describes. ric topology. Traditionally, the only topology an undergraduate might see is point-set topology at a fairly abstract level. The next course the average stu dent would take would be a graduate course in algebraic topology, and such courses are commonly very homological in nature, providing quick access to current research, but not developing any intuition or geometric sense. I have tried in this text to provide the undergraduate with a pragmatic introduction to the field, including a sampling from point-set, geometric, and algebraic topology, and trying not to include anything that the student cannot immediately experience. The exercises are to be considered as an in tegral part of the text and, ideally, should be addressed when they are met, rather than at the end of a block of material. Many of them are quite easy and are intended to give the student practice working with the definitions and digesting the current topic before proceeding. The appendix provides a brief survey of the group theory needed.

Lectures on Algebraic Topology

Author: Sergeĭ Vladimirovich Matveev

Publisher: European Mathematical Society

ISBN: 9783037190234

Category: Algebraic topology

Page: 99

View: 3434

Algebraic topology is the study of the global properties of spaces by means of algebra. It is an important branch of modern mathematics with a wide degree of applicability to other fields, including geometric topology, differential geometry, functional analysis, differential equations, algebraic geometry, number theory, and theoretical physics. This book provides an introduction to the basic concepts and methods of algebraic topology for the beginner. It presents elements of both homology theory and homotopy theory, and includes various applications. The author's intention is to rely on the geometric approach by appealing to the reader's own intuition to help understanding. The numerous illustrations in the text also serve this purpose. Two features make the text different from the standard literature: first, special attention is given to providing explicit algorithms for calculating the homology groups and for manipulating the fundamental groups. Second, the book contains many exercises, all of which are supplied with hints or solutions. This makes the book suitable for both classroom use and for independent study.

Handbook of Discrete and Computational Geometry, Third Edition

Author: Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman

Publisher: CRC Press

ISBN: 1351645919

Category: Computers

Page: 1928

View: 8775

The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in ?elds as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed signi?cantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young ?eld of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Computational Topology

An Introduction

Author: Herbert Edelsbrunner,John Harer

Publisher: American Mathematical Soc.

ISBN: 0821849255

Category: Mathematics

Page: 241

View: 695

Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.

Understanding Topology

A Practical Introduction

Author: Shaun V. Ault

Publisher: JHU Press

ISBN: 142142407X

Category: Mathematics

Page: 416

View: 4610

"Topology can present significant challenges for undergraduate students of mathematics and the sciences. 'Understanding topology' aims to change that. The perfect introductory topology textbook, 'Understanding topology' requires only a knowledge of calculus and a general familiarity with set theory and logic. Equally approachable and rigorous, the book's clear organization, worked examples, and concise writing style support a thorough understanding of basic topological principles. Professor Shaun V. Ault's unique emphasis on fascinating applications, from chemical dynamics to determining the shape of the universe, will engage students in a way traditional topology textbooks do not"--

Fundamental Neuroscience

Author: Larry R. Squire

Publisher: Academic Press

ISBN: 0123858704

Category: Medical

Page: 1127

View: 5176

Fundamental Neuroscience, 3rd Edition introduces graduate and upper-level undergraduate students to the full range of contemporary neuroscience. Addressing instructor and student feedback on the previous edition, all of the chapters are rewritten to make this book more concise and student-friendly than ever before. Each chapter is once again heavily illustrated and provides clinical boxes describing experiments, disorders, and methodological approaches and concepts. A companion web site contains test questions, and an imagebank of the figures for ready use in presentations, slides, and handouts. Capturing the promise and excitement of this fast-moving field, Fundamental Neuroscience, 3rd Edition is the text that students will be able to reference throughout their neuroscience careers! New to this edition: * 30% new material including new chapters on Dendritic Development and Spine Morphogenesis, Chemical Senses, Cerebellum, Eye Movements, Circadian Timing, Sleep and Dreaming, and Consciousness * Companion website with figures, web links to additional material, and test questions * Additional text boxes describing key experiments, disorders, methods, and concepts * Multiple model system coverage beyond rats, mice, and monkeys * Extensively expanded index for easier referencing

A Concise Course in Algebraic Topology

Author: J. P. May

Publisher: University of Chicago Press

ISBN: 9780226511832

Category: Mathematics

Page: 243

View: 5446

Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.

Molecular Biology of the Cell

Author: Bruce Alberts

Publisher: Garland Science

ISBN: 1317563743

Category: Science

Page: 1464

View: 6565

As the amount of information in biology expands dramatically, it becomes increasingly important for textbooks to distill the vast amount of scientific knowledge into concise principles and enduring concepts.As with previous editions, Molecular Biology of the Cell, Sixth Edition accomplishes this goal with clear writing and beautiful illustrations. The Sixth Edition has been extensively revised and updated with the latest research in the field of cell biology, and it provides an exceptional framework for teaching and learning. The entire illustration program has been greatly enhanced.Protein structures better illustrate structure–function relationships, icons are simpler and more consistent within and between chapters, and micrographs have been refreshed and updated with newer, clearer, or better images. As a new feature, each chapter now contains intriguing openended questions highlighting “What We Don’t Know,” introducing students to challenging areas of future research. Updated end-of-chapter problems reflect new research discussed in the text, and these problems have been expanded to all chapters by adding questions on developmental biology, tissues and stem cells, pathogens, and the immune system.

Graph Algorithms

Author: Shimon Even

Publisher: Cambridge University Press

ISBN: 1139504150

Category: Computers

Page: N.A

View: 3517

Shimon Even's Graph Algorithms, published in 1979, was a seminal introductory book on algorithms read by everyone engaged in the field. This thoroughly revised second edition, with a foreword by Richard M. Karp and notes by Andrew V. Goldberg, continues the exceptional presentation from the first edition and explains algorithms in a formal but simple language with a direct and intuitive presentation. The book begins by covering basic material, including graphs and shortest paths, trees, depth-first-search and breadth-first search. The main part of the book is devoted to network flows and applications of network flows, and it ends with chapters on planar graphs and testing graph planarity.

Groups Acting on Graphs

Author: Warren Dicks,M. J. Dunwoody

Publisher: Cambridge University Press

ISBN: 9780521230339

Category: Mathematics

Page: 283

View: 4595

Originally published in 1989, this is an advanced text and research monograph on groups acting on low-dimensional topological spaces, and for the most part the viewpoint is algebraic. Much of the book occurs at the one-dimensional level, where the topology becomes graph theory. Two-dimensional topics include the characterization of Poincare duality groups and accessibility of almost finitely presented groups. The main three-dimensional topics are the equivariant loop and sphere theorems. The prerequisites grow as the book progresses up the dimensions. A familiarity with group theory is sufficient background for at least the first third of the book, while the later chapters occasionally state without proof and then apply various facts which require knowledge of homological algebra and algebraic topology. This book is essential reading for anyone contemplating working in the subject.

Real and Complex Singularities

Author: Ana Claudia Nabarro,Juan J. Nuño-Ballesteros,Raúl Oset Sinha,Maria Aparecida Soares Ruas

Publisher: American Mathematical Soc.

ISBN: 1470422050

Category: Differential geometry -- Classical differential geometry -- Classical differential geometry

Page: 355

View: 3040

This volume is a collection of papers presented at the XIII International Workshop on Real and Complex Singularities, held from July 27–August 8, 2014, in São Carlos, Brazil, in honor of María del Carmen Romero Fuster's 60th birthday. The volume contains the notes from two mini-courses taught during the workshop: on intersection homology by J.-P. Brasselet, and on non-isolated hypersurface singularities and Lê cycles by D. Massey. The remaining contributions are research articles which cover topics from the foundations of singularity theory (including classification theory and invariants) to topology of singular spaces (links of singularities and semi-algebraic sets), as well as applications to topology (cobordism and Lefschetz fibrations), dynamical systems (Morse-Bott functions) and differential geometry (affine geometry, Gauss-maps, caustics, frontals and non-Euclidean geometries). This book is published in cooperation with Real Sociedad Matemática Española (RSME)

Surface Production Operations, Volume 1

Design of Oil Handling Systems and Facilities

Author: Maurice Stewart,Ken E. Arnold

Publisher: Elsevier

ISBN: 9780080555072

Category: Technology & Engineering

Page: 768

View: 5801

The latest edition of this best-selling title is updated and expanded for easier use by engineers. New to this edition is a section on the fundamentals of surface production operations taking up topics from the oilfield as originally planned by the authors in the first edition. This information is necessary and endemic to production and process engineers. Now, the book offers a truly complete picture of surface production operations, from the production stage to the process stage with applications to process and production engineers. · New in-depth coverage of hydrocarbon characteristics, the different kinds of reservoirs, and impurities in crude. · Practical suggestions help readers understand the art and science of handling produced liquids. · Numerous, easy-to-read figures, charts, tables, and photos clearly explain how to design, specify, and operate oilfield surface production facilities.

Bioreaction Engineering Principles

Second Edition

Author: Jens Nielsen,John Villadsen,Gunnar Lidén

Publisher: Springer

ISBN: 1461507677

Category: Technology & Engineering

Page: 528

View: 3813

This is the second edition of the text "Bioreaction Engineering Principles" by Jens Nielsen and John Villadsen, originally published in 1994 by Plenum Press (now part of Kluwer). Time runs fast in Biotechnology, and when Kluwer Plenum stopped reprinting the first edition and asked us to make a second, revised edition we happily accepted. A text on bioreactions written in the early 1990's will not reflect the enormous development of experimental as well as theoretical aspects of cellular reactions during the past decade. In the preface to the first edition we admitted to be newcomers in the field. One of us (JV) has had 10 more years of job training in biotechnology, and the younger author (IN) has now received international recognition for his work with the hottest topics of "modem" biotechnology. Furthermore we are happy to have induced Gunnar Liden, professor of chemical reaction engineering at our sister university in Lund, Sweden to join us as co-author of the second edition. His contribution, especially on the chemical engineering aspects of "real" bioreactors has been of the greatest value. Chapter 8 of the present edition is largely unchanged from the first edition. We wish to thank professor Martin Hjortso from LSU for his substantial help with this chapter.

Multiple View Geometry in Computer Vision

Author: Richard Hartley,Andrew Zisserman

Publisher: Cambridge University Press

ISBN: 1139449141

Category: Computers

Page: N.A

View: 6748

A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.

Computational Algebraic Geometry

Author: Frederic Eyssette,Andre Galligo

Publisher: Springer Science & Business Media

ISBN: 1461227526

Category: Mathematics

Page: 332

View: 7716

Understanding DNA

The Molecule and How it Works

Author: Chris R. Calladine,Horace Drew,Ben Luisi,Andrew Travers

Publisher: Elsevier

ISBN: 9780080474663

Category: Science

Page: 352

View: 6507

The functional properties of any molecule are directly related to, and affected by, its structure. This is especially true for DNA, the molecular that carries the code for all life on earth. The third edition of Understanding DNA has been entirely revised and updated, and expanded to cover new advances in our understanding. It explains, step by step, how DNA forms specific structures, the nature of these structures and how they fundamentally affect the biological processes of transcription and replication. Written in a clear, concise and lively fashion, Understanding DNA is essential reading for all molecular biology, biochemistry and genetics students, to newcomers to the field from other areas such as chemistry or physics, and even for seasoned researchers, who really want to understand DNA. Describes the basic units of DNA and how these form the double helix, and the various types of DNA double helix Outlines the methods used to study DNA structure Contains over 130 illustrations, some in full color, as well as exercises and further readings to stimulate student comprehension

The Yeasts

A Taxonomic Study

Author: Cletus Kurtzman,J.W. Fell,Teun Boekhout

Publisher: Elsevier

ISBN: 9780080931272

Category: Science

Page: 2354

View: 8882

The Yeasts: A Taxonomic Study is a three-volume book that covers the taxonomic aspect of yeasts. The main goal of this book is to provide important information about the identification of yeasts. It also discusses the growth tests that can be used to identify different species of yeasts, and it examines how the more important species of yeasts provide information for the selection of species needed for biotechnology. • Volume 1 discusses the identification, classification and importance of yeasts in the field of biotechnology. • Volume 2 focuses on the identification and classification of ascomycetous yeasts. • Volume 3 deals with the identification and classification of basidiomycetous yeasts, along with the genus Prototheca. High-quality photomicrographs and line drawings Detailed phylogenetic trees Up-to-date, clearly presented yeast taxonomy and systematic, easy-to-use reference sequence accession numbers to allow for correct identification