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

Graphs, Surfaces and Homology: An Introduction to Algebraic Topology

P. J. Giblin (auth.)
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ჩატვირთეთ, ხარისხის შესაფასებლად
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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.

კატეგორია:
წელი:
1981
გამოცემა:
2nd Edition
გამომცემლობა:
Springer Netherlands
ენა:
english
გვერდები:
329
ISBN 10:
9400959532
ISBN 13:
9789400959538
სერია:
Chapman and Hall Mathematics Series
ფაილი:
PDF, 22.24 MB
IPFS:
CID , CID Blake2b
english, 1981
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