Author : Robert M. Switzer
Publisher : Springer
Page : 541 pages
File Size : 20,10 MB
Release : 2017-12-01
Category : Mathematics
ISBN : 3642619231
From the reviews: "The author has attempted an ambitious and most commendable project. [...] The book contains much material that has not previously appeared in this format. The writing is clean and clear and the exposition is well motivated. [...] This book is, all in all, a very admirable work and a valuable addition to the literature." Mathematical Reviews
Author : Robert M. Switzer
Publisher : Boom Koninklijke Uitgevers
Page : 552 pages
File Size : 18,60 MB
Release : 2002-01-10
Category : Mathematics
ISBN : 9783540427506
From the reviews: "The author has attempted an ambitious and most commendable project. [...] The book contains much material that has not previously appeared in this format. The writing is clean and clear and the exposition is well motivated. [...] This book is, all in all, a very admirable work and a valuable addition to the literature." Mathematical Reviews
Author : C. R. F. Maunder
Publisher : Courier Corporation
Page : 414 pages
File Size : 22,49 MB
Release : 1996-01-01
Category : Mathematics
ISBN : 9780486691312
Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated, and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. Author C.R.F. Maunder provides examples and exercises; and notes and references at the end of each chapter trace the historical development of the subject.
Author : Tammo tom Dieck
Publisher : European Mathematical Society
Page : 584 pages
File Size : 39,12 MB
Release : 2008
Category : Mathematics
ISBN : 9783037190487
This book is written as a textbook on algebraic topology. The first part covers the material for two introductory courses about homotopy and homology. The second part presents more advanced applications and concepts (duality, characteristic classes, homotopy groups of spheres, bordism). The author recommends starting an introductory course with homotopy theory. For this purpose, classical results are presented with new elementary proofs. Alternatively, one could start more traditionally with singular and axiomatic homology. Additional chapters are devoted to the geometry of manifolds, cell complexes and fibre bundles. A special feature is the rich supply of nearly 500 exercises and problems. Several sections include topics which have not appeared before in textbooks as well as simplified proofs for some important results. Prerequisites are standard point set topology (as recalled in the first chapter), elementary algebraic notions (modules, tensor product), and some terminology from category theory. The aim of the book is to introduce advanced undergraduate and graduate (master's) students to basic tools, concepts and results of algebraic topology. Sufficient background material from geometry and algebra is included.
Author : Marcelo Aguilar
Publisher : Springer Science & Business Media
Page : 499 pages
File Size : 50,88 MB
Release : 2008-02-02
Category : Mathematics
ISBN : 0387224890
The authors present introductory material in algebraic topology from a novel point of view in using a homotopy-theoretic approach. This carefully written book can be read by any student who knows some topology, providing a useful method to quickly learn this novel homotopy-theoretic point of view of algebraic topology.
Author : Lynn Arthur Steen
Publisher : Courier Corporation
Page : 274 pages
File Size : 50,81 MB
Release : 2013-04-22
Category : Mathematics
ISBN : 0486319296
Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography.
Author : James W. Vick
Publisher : Springer Science & Business Media
Page : 258 pages
File Size : 28,20 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461208815
This introduction to some basic ideas in algebraic topology is devoted to the foundations and applications of homology theory. After the essentials of singular homology and some important applications are given, successive topics covered include attaching spaces, finite CW complexes, cohomology products, manifolds, Poincare duality, and fixed point theory. This second edition includes a chapter on covering spaces and many new exercises.
Author : John Frank Adams
Publisher : University of Chicago Press
Page : 384 pages
File Size : 18,93 MB
Release : 1974
Category : Mathematics
ISBN : 0226005240
J. Frank Adams, the founder of stable homotopy theory, gave a lecture series at the University of Chicago in 1967, 1970, and 1971, the well-written notes of which are published in this classic in algebraic topology. The three series focused on Novikov's work on operations in complex cobordism, Quillen's work on formal groups and complex cobordism, and stable homotopy and generalized homology. Adams's exposition of the first two topics played a vital role in setting the stage for modern work on periodicity phenomena in stable homotopy theory. His exposition on the third topic occupies the bulk of the book and gives his definitive treatment of the Adams spectral sequence along with many detailed examples and calculations in KU-theory that help give a feel for the subject.
Author : J. P. May
Publisher : University of Chicago Press
Page : 262 pages
File Size : 12,52 MB
Release : 1999-09
Category : Mathematics
ISBN : 9780226511832
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.
Author : Robert E. Mosher
Publisher : Courier Corporation
Page : 226 pages
File Size : 25,15 MB
Release : 2008-01-01
Category : Mathematics
ISBN : 0486466647
Cohomology operations are at the center of a major area of activity in algebraic topology. This treatment explores the single most important variety of operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications, including several different techniques of homotopy theory useful for computation. 1968 edition.
