Graphs, Surfaces, and Homology: An Introduction to Algebraic Topology

Giblin, P J

ISBN 10: 0470989947 / ISBN 13: 9780470989944

Published by Chapman & Hall, 1977

About this Item

Very good. No dust jacket as issued. 329 p. Outline Studies in Biology. Audience: General/trade.

Seller Inventory # Alibris5269

Bibliographic Details

• Title: Graphs, Surfaces, and Homology: An Introduction to Algebraic Topology
• Publisher: Chapman & Hall
• Publication Date: 1977
• Language: English
• ISBN 10: 0470989947
• ISBN 13: 9780470989944
• Binding: Trade paperback
• Condition: Very Good

About this title

Synopsis

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."