Algebraic Topology An Introduction

Author: William S. Massey
Publisher: Springer
ISBN: 9780387902715
Release Date: 1989-10-19
Genre: Mathematics

William S. Massey Professor Massey, born in Illinois in 1920, received his bachelor's degree from the University of Chicago and then served for four years in the U.S. Navy during World War II. After the War he received his Ph.D. from Princeton University and spent two additional years there as a post-doctoral research assistant. He then taught for ten years on the faculty of Brown University, and moved to his present position at Yale in 1960. He is the author of numerous research articles on algebraic topology and related topics. This book developed from lecture notes of courses taught to Yale undergraduate and graduate students over a period of several years.

An Introduction to Algebraic Topology

Author: Joseph J. Rotman
Publisher: Springer Science & Business Media
ISBN: 9781461245766
Release Date: 2013-11-11
Genre: Mathematics

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.

A Basic Course in Algebraic Topology

Author: W.S. Massey
Publisher: Springer Science & Business Media
ISBN: 038797430X
Release Date: 1991-01-01
Genre: Mathematics

This book provides a systematic treatment of the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. It avoids all unnecessary definitions, terminology, and technical machinery. Wherever possible, the book emphasizes the geometric motivation behind the various concepts.

Homology Theory

Author: James W. Vick
Publisher: Springer Science & Business Media
ISBN: 9781461208815
Release Date: 2012-12-06
Genre: Mathematics

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.

An Introduction to Algebraic Topology

Author: Andrew H. Wallace
Publisher: Courier Corporation
ISBN: 9780486152950
Release Date: 2011-11-30
Genre: Mathematics

This self-contained treatment begins with three chapters on the basics of point-set topology, after which it proceeds to homology groups and continuous mapping, barycentric subdivision, and simplicial complexes. 1961 edition.

Homology Theory

Author: P. J. Hilton
Publisher: CUP Archive
ISBN: 0521094224
Release Date: 1967
Genre: Mathematics

This account of algebraic topology is complete in itself, assuming no previous knowledge of the subject. It is used as a textbook for students in the final year of an undergraduate course or on graduate courses and as a handbook for mathematicians in other branches who want some knowledge of the subject.

Algebraic Topology

Author: Rafael Ayala
Publisher: Alpha Science International Limited
ISBN: 1842657364
Release Date: 2012
Genre: Mathematics

ALGEBRAIC TOPOLOGY: An Introduction starts with the combinatorial definition of simplicial (co) homology and its main properties (including duality for homology manifolds). Then the geometrical facet of (co) homology via bordism theory is sketched and it is shown that the corresponding theory for pseudomanifolds coincides with the homology obtained from the singular chain complex. The classical applications of (co) homology theory are included. Degree and fixed-point theory are presented with their extensions to infinite dimensional spaces. The book also contains a geometric approach to the Hurewicz theorem relating homology and homotopy. The last chapter exploits the algebraic invariants introduced in the book to give in detail the homotopical classification of the three-dimensional lens spaces. Each chapter concludes with a generous list of exercises and problems; many of them contain hints for their solution. Some groups of problems introduce a topic not included in the basic core of the book.

Introduction to Differential and Algebraic Topology

Author: Yu.G. Borisovich
Publisher: Springer Science & Business Media
ISBN: 9789401719599
Release Date: 2013-03-09
Genre: Mathematics

Topology as a subject, in our opinion, plays a central role in university education. It is not really possible to design courses in differential geometry, mathematical analysis, differential equations, mechanics, functional analysis that correspond to the temporary state of these disciplines without involving topological concepts. Therefore, it is essential to acquaint students with topo logical research methods already in the first university courses. This textbook is one possible version of an introductory course in topo logy and elements of differential geometry, and it absolutely reflects both the authors' personal preferences and experience as lecturers and researchers. It deals with those areas of topology and geometry that are most closely related to fundamental courses in general mathematics. The educational material leaves a lecturer a free choice in designing his own course or his own seminar. We draw attention to a number of particularities in our book. The first chap ter, according to the authors' intention, should acquaint readers with topolo gical problems and concepts which arise from problems in geometry, analysis, and physics. Here, general topology (Ch. 2) is presented by introducing con structions, for example, related to the concept of quotient spaces, much earlier than various other notions of general topology thus making it possible for students to study important examples of manifolds (two-dimensional surfaces, projective spaces, orbit spaces, etc.) as topological spaces, immediately.

A First Course in Algebraic Topology

Author: Czes Kosniowski
Publisher: CUP Archive
ISBN: 0521298644
Release Date: 1980-09-25
Genre: Mathematics

This self-contained introduction to algebraic topology is suitable for a number of topology courses. It consists of about one quarter 'general topology' (without its usual pathologies) and three quarters 'algebraic topology' (centred around the fundamental group, a readily grasped topic which gives a good idea of what algebraic topology is). The book has emerged from courses given at the University of Newcastle-upon-Tyne to senior undergraduates and beginning postgraduates. It has been written at a level which will enable the reader to use it for self-study as well as a course book. The approach is leisurely and a geometric flavour is evident throughout. The many illustrations and over 350 exercises will prove invaluable as a teaching aid. This account will be welcomed by advanced students of pure mathematics at colleges and universities.

Topology

Author: Donald W. Kahn
Publisher: Courier Corporation
ISBN: 0486686094
Release Date: 1995
Genre: Mathematics

Comprehensive coverage of elementary general topology as well as algebraic topology, specifically 2-manifolds, covering spaces and fundamental groups. Problems, with selected solutions. Bibliography. 1975 edition.

Topology

Author: Stefan Waldmann
Publisher: Springer
ISBN: 9783319096803
Release Date: 2014-08-05
Genre: Mathematics

This book provides a concise introduction to topology and is necessary for courses in differential geometry, functional analysis, algebraic topology, etc. Topology is a fundamental tool in most branches of pure mathematics and is also omnipresent in more applied parts of mathematics. Therefore students will need fundamental topological notions already at an early stage in their bachelor programs. While there are already many excellent monographs on general topology, most of them are too large for a first bachelor course. Topology fills this gap and can be either used for self-study or as the basis of a topology course.

Algebraic Topology

Author: William Fulton
Publisher: Springer Science & Business Media
ISBN: 9781461241805
Release Date: 2013-12-01
Genre: Mathematics

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