Graphs, surfaces and homology / Peter Giblin.

Format:

Book

Author/Creator:

Giblin, P. J., author.

Language:

English

Subjects (All):

Algebraic topology.

Physical Description:

1 online resource (xx, 251 pages) : digital, PDF file(s).

Edition:

Third edition.

Other Title:

Graphs, Surfaces & Homology

Place of Publication:

Cambridge : Cambridge University Press, 2010.

Language Note:

English

Summary:

Homology theory is a powerful algebraic tool that is at the centre of current research in topology and its applications. This accessible textbook will appeal to mathematics students interested in the application of algebra to geometrical problems, specifically the study of surfaces (sphere, torus, Mobius band, Klein bottle). In this introduction to simplicial homology - the most easily digested version of homology theory - the author studies interesting geometrical problems, such as the structure of two-dimensional surfaces and the embedding of graphs in surfaces, using the minimum of algebraic machinery and including a version of Lefschetz duality. Assuming very little mathematical knowledge, the book provides a complete account of the algebra needed (abelian groups and presentations), and the development of the material is always carefully explained with proofs given in full detail. Numerous examples and exercises are also included, making this an ideal text for undergraduate courses or for self-study.

Contents:

Introduction

Graphs

Closed surfaces

Simplicial complexes

Homology groups

The question of invariance

Some general theorems

Two more general theorems

Homology modulo 2

Graphs in surfaces

Appendix. Abelian groups.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-107-20890-4

1-282-77149-3

9786612771491

0-511-77953-4

0-511-90140-2

0-511-90219-0

0-511-79904-7

0-511-79764-8

0-511-90061-9

OCLC:

663861936