{"product_id":"graphs-surfaces-and-homology-an-introduction-to-algebraic-topology-chapman-and-hall-mathematics-series-0412239000","title":"Graphs, Surfaces and Homology: An Introduction to Algebraic Topology (Chapman and Hall Mathematics Series)","description":"\u003cp\u003e\u003cstrong\u003eISBN:\u003c\/strong\u003e 0412239000\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAuthor:\u003c\/strong\u003e Giblin, P.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eCondition:\u003c\/strong\u003e New\u003c\/p\u003e\u003cp\u003eviii 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.\u003c\/p\u003e","brand":"Mia Karts","offers":[{"title":"Default Title","offer_id":51856970383648,"sku":"NEW0412239000","price":61.33,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0980\/7426\/3840\/files\/51642juLROL.jpg?v=1781552360","url":"https:\/\/miakarts.com\/products\/graphs-surfaces-and-homology-an-introduction-to-algebraic-topology-chapman-and-hall-mathematics-series-0412239000","provider":"Miakarts Books","version":"1.0","type":"link"}