Fundamentals Of Algebraic Topology
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Author |
: Steven H. Weintraub |
Publisher |
: Springer |
Total Pages |
: 169 |
Release |
: 2014-10-31 |
ISBN-10 |
: 9781493918447 |
ISBN-13 |
: 1493918443 |
Rating |
: 4/5 (47 Downloads) |
Synopsis Fundamentals of Algebraic Topology by : Steven H. Weintraub
This rapid and concise presentation of the essential ideas and results of algebraic topology follows the axiomatic foundations pioneered by Eilenberg and Steenrod. The approach of the book is pragmatic: while most proofs are given, those that are particularly long or technical are omitted, and results are stated in a form that emphasizes practical use over maximal generality. Moreover, to better reveal the logical structure of the subject, the separate roles of algebra and topology are illuminated. Assuming a background in point-set topology, Fundamentals of Algebraic Topology covers the canon of a first-year graduate course in algebraic topology: the fundamental group and covering spaces, homology and cohomology, CW complexes and manifolds, and a short introduction to homotopy theory. Readers wishing to deepen their knowledge of algebraic topology beyond the fundamentals are guided by a short but carefully annotated bibliography.
Author |
: F.H. Croom |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 187 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781468494754 |
ISBN-13 |
: 1468494759 |
Rating |
: 4/5 (54 Downloads) |
Synopsis Basic Concepts of Algebraic Topology by : F.H. Croom
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.
Author |
: Samuel Eilenberg |
Publisher |
: Princeton University Press |
Total Pages |
: 345 |
Release |
: 2015-12-08 |
ISBN-10 |
: 9781400877492 |
ISBN-13 |
: 1400877490 |
Rating |
: 4/5 (92 Downloads) |
Synopsis Foundations of Algebraic Topology by : Samuel Eilenberg
The need for an axiomatic treatment of homology and cohomology theory has long been felt by topologists. Professors Eilenberg and Steenrod present here for the first time an axiomatization of the complete transition from topology to algebra. Originally published in 1952. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author |
: Steven Weintraub |
Publisher |
: Springer |
Total Pages |
: 163 |
Release |
: 2014-11-01 |
ISBN-10 |
: 1493918451 |
ISBN-13 |
: 9781493918454 |
Rating |
: 4/5 (51 Downloads) |
Synopsis Fundamentals of Algebraic Topology by : Steven Weintraub
This rapid and concise presentation of the essential ideas and results of algebraic topology follows the axiomatic foundations pioneered by Eilenberg and Steenrod. The approach of the book is pragmatic: while most proofs are given, those that are particularly long or technical are omitted, and results are stated in a form that emphasizes practical use over maximal generality. Moreover, to better reveal the logical structure of the subject, the separate roles of algebra and topology are illuminated. Assuming a background in point-set topology, Fundamentals of Algebraic Topology covers the canon of a first-year graduate course in algebraic topology: the fundamental group and covering spaces, homology and cohomology, CW complexes and manifolds, and a short introduction to homotopy theory. Readers wishing to deepen their knowledge of algebraic topology beyond the fundamentals are guided by a short but carefully annotated bibliography.
Author |
: |
Publisher |
: |
Total Pages |
: 304 |
Release |
: 2014 |
ISBN-10 |
: 8126162406 |
ISBN-13 |
: 9788126162406 |
Rating |
: 4/5 (06 Downloads) |
Synopsis Fundamentals of Algebraic Topology by :
Author |
: Mahima Ranjan Adhikari |
Publisher |
: Springer |
Total Pages |
: 628 |
Release |
: 2016-09-16 |
ISBN-10 |
: 9788132228431 |
ISBN-13 |
: 813222843X |
Rating |
: 4/5 (31 Downloads) |
Synopsis Basic Algebraic Topology and its Applications by : Mahima Ranjan Adhikari
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.
Author |
: J. P. May |
Publisher |
: University of Chicago Press |
Total Pages |
: 262 |
Release |
: 1999-09 |
ISBN-10 |
: 0226511839 |
ISBN-13 |
: 9780226511832 |
Rating |
: 4/5 (39 Downloads) |
Synopsis A Concise Course in Algebraic Topology by : J. P. May
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 |
: Anant R. Shastri |
Publisher |
: CRC Press |
Total Pages |
: 552 |
Release |
: 2016-02-03 |
ISBN-10 |
: 9781466562448 |
ISBN-13 |
: 1466562447 |
Rating |
: 4/5 (48 Downloads) |
Synopsis Basic Algebraic Topology by : Anant R. Shastri
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
Author |
: Joseph J. Rotman |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 447 |
Release |
: 2013-11-11 |
ISBN-10 |
: 9781461245766 |
ISBN-13 |
: 1461245761 |
Rating |
: 4/5 (66 Downloads) |
Synopsis An Introduction to Algebraic Topology by : Joseph J. Rotman
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.
Author |
: James F. Davis |
Publisher |
: American Mathematical Society |
Total Pages |
: 385 |
Release |
: 2023-05-22 |
ISBN-10 |
: 9781470473686 |
ISBN-13 |
: 1470473682 |
Rating |
: 4/5 (86 Downloads) |
Synopsis Lecture Notes in Algebraic Topology by : James F. Davis
The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the “big picture”, teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.