Graphs, Surfaces and Homology: Introduction to Algebraic Topology - Softcover

P.J. Giblin

Softcover

ISBN 10: 0412214407 ISBN 13: 9780412214400

Publisher: Chapman and Hall, 1977

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.

Edition details

• Publisher: Chapman and Hall
• Publication date: 1977
• ISBN 10: 0412214407
• ISBN 13: 9780412214400
• Binding: Paperback
• Language: English
• Edition number: 2
• Number of pages: 352