Graphs, Surfaces and Homology: An Introduction to Algebraic Topology (Chapman and Hall Mathematics Series)

Giblin, P.

ISBN 10: 0412239000 / ISBN 13: 9780412239007

Edité par Springer, 1981

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Détails bibliographiques

• Titre: Graphs, Surfaces and Homology: An Introduction to Algebraic Topology (Chapman and Hall Mathematics Series)
• Éditeur: Springer
• Date de parution: 1981
• Langue: anglais
• ISBN à 10 chiffres: 0412239000
• ISBN à 13 chiffres: 9780412239007
• Reliure: Couverture souple
• État de l'article: New

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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.