9780412239007 - graphs, surfaces and homology: an introduction to algebraic topology (chapman and hall mathematics series) von giblin, p. (5 Ergebnisse)
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Zustand: New. Series: Chapman and Hall Mathematics Series (Closed). Num Pages: 346 pages, 41 black & white illustrations, biography. BIC Classification: PBPD. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 216 x 140 x 18. Weight in Grams: 443. . 1981. 2 Rev ed. Pa…perback. . . . . Books ship from the US and Ireland.
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.
