An Introduction To Algebraic Topology

Author: Joseph J. Rotman
Editor: Springer Science & Business Media
ISBN: 1461245761
Size: 20,67 MB
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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.

An Introduction To Algebraic Topology

Author: Andrew H. Wallace
Editor: Courier Corporation
ISBN: 0486152952
Size: 10,94 MB
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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
Editor: CUP Archive
ISBN: 9780521094221
Size: 18,10 MB
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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.

Homology Theory

Author: James W. Vick
Editor: Springer Science & Business Media
ISBN: 1461208815
Size: 14,94 MB
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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.

Homotopy Theory An Introduction To Algebraic Topology

Author:
Editor: Academic Press
ISBN: 9780080873800
Size: 12,57 MB
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Homotopy Theory: An Introduction to Algebraic Topology

An Introduction To Algebraic Topology

Author: John W. Keesee
Editor:
ISBN:
Size: 18,51 MB
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Topology

Author: Donald W. Kahn
Editor: Courier Corporation
ISBN: 9780486686097
Size: 18,21 MB
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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.

A Basic Course In Algebraic Topology

Author: William S. Massey
Editor: Springer
ISBN: 1493990632
Size: 14,86 MB
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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.

Graphs Surfaces And Homology

Author: P. Giblin
Editor: Springer Science & Business Media
ISBN: 9400959532
Size: 14,73 MB
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viii homology groups. A weaker result, sufficient nevertheless for our purposes, is proved in Chapter 5, where the reader will also find some discussion of the need for a more powerful in variance theorem and a summary of the proof of such a theorem. Secondly the emphasis in this book is on low-dimensional examples the graphs and surfaces of the title since it is there that geometrical intuition has its roots. The goal of the book is the investigation in Chapter 9 of the properties of graphs in surfaces; some of the problems studied there are mentioned briefly in the Introduction, which contains an in formal survey of the material of the book. Many of the results of Chapter 9 do indeed generalize to higher dimensions (and the general machinery of simplicial homology theory is avai1able from earlier chapters) but I have confined myself to one example, namely the theorem that non-orientable closed surfaces do not embed in three-dimensional space. One of the principal results of Chapter 9, a version of Lefschetz duality, certainly generalizes, but for an effective presentation such a gener- ization needs cohomology theory. Apart from a brief mention in connexion with Kirchhoff's laws for an electrical network I do not use any cohomology here. Thirdly there are a number of digressions, whose purpose is rather to illuminate the central argument from a slight dis tance, than to contribute materially to its exposition.

A First Course In Algebraic Topology

Author: Czes Kosniowski
Editor: CUP Archive
ISBN: 9780521298643
Size: 11,66 MB
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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.