{"product_id":"9780412239007","title":"Chapman and Hall Mathematics Series: An Introduction to Algebraic Topology","description":"\u003ch1\u003eChapman and Hall Mathematics Series: An Introduction to Algebraic Topology\u003c\/h1\u003e \u003ch2\u003eGiblin, P.\u003c\/h2\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 \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 1981-10-29\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9780412239007\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-94-009-5953-8\u003c\/p\u003e \u003cp\u003eDimensions: 216cm x140cm\u003c\/p\u003e \u003cp\u003ePages: 329\u003c\/p\u003e ","brand":"Springer Netherlands","offers":[{"title":"Default Title","offer_id":44448572899468,"sku":"9780412239007","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9780412239007.jpg?v=1775817655","url":"https:\/\/lateknightbooks.com\/products\/9780412239007","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}