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: William S. Massey
Publisher: Springer Science & Business Media
ISBN: 038797430X
Release Date: 1991
Genre: Mathematics

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.

Algebraic Topology

Author:
Publisher: 清华大学出版社有限公司
ISBN: 730210588X
Release Date: 2002
Genre: Algebraic topology


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.

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.

Lectures on Algebraic Topology

Author: Albrecht Dold
Publisher: Springer Science & Business Media
ISBN: 3540586601
Release Date: 1995-02-15
Genre: Mathematics

Springer is reissuing a selected few highly successful books in a new, inexpensive softcover edition to make them easily accessible to younger generations of students and researchers. Springer-Verlag began publishing books in higher mathematics in 1920. This is a reprint of the Second Edition.

Algebraic Topology

Author: Edwin H. Spanier
Publisher: Springer Science & Business Media
ISBN: 9781468493221
Release Date: 2012-12-06
Genre: Mathematics

This book surveys the fundamental ideas of algebraic topology. The first part covers the fundamental group, its definition and application in the study of covering spaces. The second part turns to homology theory including cohomology, cup products, cohomology operations and topological manifolds. The final part is devoted to Homotropy theory, including basic facts about homotropy groups and applications to obstruction theory.

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.

Computational Topology

Author: Herbert Edelsbrunner
Publisher: American Mathematical Soc.
ISBN: 9780821849255
Release Date: 2010
Genre: Mathematics

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.

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

Algebraic Topology

Author: C. R. F. Maunder
Publisher: Courier Corporation
ISBN: 0486691314
Release Date: 1996
Genre: Mathematics

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.

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.