## A Basic Course In Algebraic Topology

**Author**: William S. Massey

**Editor:**Springer

**ISBN:**1493990632

**Size**: 12,44 MB

**Format:**PDF, Docs

**Read:**188

This textbook is intended for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. The text consists of material from the first five chapters of the author's earlier book, Algebraic Topology; an Introduction (GTM 56) together with almost all of his book, Singular Homology Theory (GTM 70). The material from the two earlier books has been substantially revised, corrected, and brought up to date.

## A Basic Course In Algebraic Topology

**Author**: William S. Massey

**Editor:**Springer

**ISBN:**9783540974307

**Size**: 15,54 MB

**Format:**PDF, ePub, Mobi

**Read:**999

## A Concise Course In Algebraic Topology

**Author**: J. P. May

**Editor:**University of Chicago Press

**ISBN:**9780226511832

**Size**: 11,21 MB

**Format:**PDF, ePub, Docs

**Read:**113

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.

## Algebraic Topology

**Author**: Allen Hatcher

**Editor:**Cambridge University Press

**ISBN:**9780521795401

**Size**: 12,38 MB

**Format:**PDF, Kindle

**Read:**692

An introductory textbook suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises.

## A First Course In Algebraic Topology

**Author**: B. K. Lahiri

**Editor:**Alpha Science International Limited

**ISBN:**9781842652268

**Size**: 17,91 MB

**Format:**PDF, Kindle

**Read:**964

Includes basic notions of category, functors and homotopy of continuous mappings including relative homotopy. In this book, simplexes and complexes are presented in detail and two homology theories-simplicial homology and singular homology have been considered along with calculations of some homology groups.

## An Introduction To Algebraic Topology

**Author**: Joseph J. Rotman

**Editor:**Springer Science & Business Media

**ISBN:**1461245761

**Size**: 19,36 MB

**Format:**PDF, ePub, Mobi

**Read:**354

A clear exposition, with exercises, of the basic ideas of algebraic topology. Suitable for a two-semester course at the beginning graduate level, it assumes a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced.

## Basic Algebraic Topology

**Author**: Anant R. Shastri

**Editor:**CRC Press

**ISBN:**1466562447

**Size**: 15,36 MB

**Format:**PDF, Docs

**Read:**517

Building on rudimentary knowledge of real analysis, point-set topology, and basic algebra, Basic Algebraic Topology provides plenty of material for a two-semester course in algebraic topology. The book first introduces the necessary fundamental concepts, such as relative homotopy, fibrations and cofibrations, category theory, cell complexes, and si

## More Concise Algebraic Topology

**Author**: J. P. May

**Editor:**University of Chicago Press

**ISBN:**0226511782

**Size**: 16,29 MB

**Format:**PDF, Kindle

**Read:**322

With firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. There are very few textbooks that treat fundamental topics beyond a first course, and many topics now essential to the field are not treated in any textbook. J. Peter May’s A Concise Course in Algebraic Topology addresses the standard first course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. In this sequel, May and his coauthor, Kathleen Ponto, cover topics that are essential for algebraic topologists and others interested in algebraic topology, but that are not treated in standard texts. They focus on the localization and completion of topological spaces, model categories, and Hopf algebras. The first half of the book sets out the basic theory of localization and completion of nilpotent spaces, using the most elementary treatment the authors know of. It makes no use of simplicial techniques or model categories, and it provides full details of other necessary preliminaries. With these topics as motivation, most of the second half of the book sets out the theory of model categories, which is the central organizing framework for homotopical algebra in general. Examples from topology and homological algebra are treated in parallel. A short last part develops the basic theory of bialgebras and Hopf algebras.

## Algebraic Topology

**Author**: William Fulton

**Editor:**Springer Science & Business Media

**ISBN:**1461241804

**Size**: 10,45 MB

**Format:**PDF, Kindle

**Read:**746

To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ ential topology, etc.), we concentrate our attention on concrete prob lems in low dimensions, introducing only as much algebraic machin ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel opment of the subject. What would we like a student to know after a first course in to pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind ing numbers and degrees of mappings, fixed-point theorems; appli cations such as the Jordan curve theorem, invariance of domain; in dices of vector fields and Euler characteristics; fundamental groups

## Basic Algebraic Topology And Its Applications

**Author**: Mahima Ranjan Adhikari

**Editor:**Springer

**ISBN:**813222843X

**Size**: 16,17 MB

**Format:**PDF

**Read:**282

This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.