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Graphs, Surfaces and Homology: An Introduction to Algebraic Topology

Graphs, Surfaces and Homology: An Introduction to Algebraic Topology

          
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About the Book

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.


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Product Details
  • ISBN-13: 9780412239007
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Edition: 0002-
  • Language: English
  • Returnable: N
  • Spine Width: 18 mm
  • Weight: 404 gr
  • ISBN-10: 0412239000
  • Publisher Date: 29 Oct 1981
  • Binding: Paperback
  • Height: 216 mm
  • No of Pages: 329
  • Series Title: Chapman and Hall Mathematics
  • Sub Title: An Introduction to Algebraic Topology
  • Width: 140 mm


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