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We would especially like to thank Chris Saunders for his dedication and en­ thusiasm concerning this project and the many helpful suggestions he made throughout the development of this text. We would also like to thank Bob Wells for sharing with us his extensive knowledge of CW-complexes, Morse theory, and singular homology. Chapters 3 and 6, in particular, benefited significantly from the many insightful conver­ sations we had with Bob Wells concerning a Morse function and its associated CW-complex.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51024513368337,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51024515891473,"sku":"NIN9781402026959","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52148381810961,"sku":"NLS9781402026959","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1402026951.jpg?v=1751146285"},{"product_id":"twisted-morse-complexes-book-augustin-banyaga-9783031716157","title":"Twisted Morse Complexes","description":"This book gives a detailed presentation of twisted Morse homology and cohomology on closed finite-dimensional smooth manifolds. It contains a complete proof of the Twisted Morse Homology Theorem, which says that on a closed finite-dimensional smooth manifold the homology of the Morse–Smale–Witten chain complex with coefficients in a bundle of abelian groups G is isomorphic to the singular homology of the manifold with coefficients in G. It also includes proofs of twisted Morse-theoretic versions of well-known theorems such as Eilenberg's Theorem, the Poincaré Lemma, and the de Rham Theorem. The effectiveness of twisted Morse complexes is demonstrated by computing the Lichnerowicz cohomology of surfaces, giving obstructions to spaces being associative H-spaces, and computing Novikov numbers.  Suitable for a graduate level course, the book may also be used as a reference for graduate students and working mathematicians or physicists.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51061979480337,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51061982200081,"sku":"NIN9783031716157","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52675645931793,"sku":"NLS9783031716157","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3031716159.jpg?v=1751252612"},{"product_id":"structure-of-classical-diffeomorphism-groups-book-augustin-banyaga-9780792344759","title":"The Structure of Classical Diffeomorphism Groups","description":"In the 60's, the work of Anderson, Chernavski, Kirby and Edwards showed that the group of homeomorphisms of a smooth manifold which are isotopic to the identity is a simple group. This led Smale to conjecture that the group Diff'\" (M)o of cr diffeomorphisms, r ~ 1, of a smooth manifold M, with compact supports, and isotopic to the identity through compactly supported isotopies, is a simple group as well. In this monograph, we give a fairly detailed proof that DifF(M)o is a simple group. This theorem was proved by Herman in the case M is the torus rn in 1971, as a consequence of the Nash-Moser-Sergeraert implicit function theorem. Thurston showed in 1974 how Herman's result on rn implies the general theorem for any smooth manifold M. The key idea was to vision an isotopy in Diff'\"(M) as a foliation on M x [0, 1]. In fact he discovered a deep connection between the local homology of the group of diffeomorphisms and the homology of the Haefliger classifying space for foliations. Thurston's paper [180] contains just a brief sketch of the proof. The details have been worked out by Mather [120], [124], [125], and the author [12]. This circle of ideas that we call the \"Thurston tricks\" is discussed in chapter 2. It explains how in certain groups of diffeomorphisms, perfectness leads to simplicity. 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This circle of ideas that we call the \"Thurston tricks\" is discussed in chapter 2. It explains how in certain groups of diffeomorphisms, perfectness leads to simplicity. 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These problems have a driving force, and have generated a great body of research, as well as insight.The main topics treated in this book include a paper by V Poenaru on the Poincaré conjecture and its ramifications, giving an insight into the herculean work of the author on the subject. Steve Armentrout's paper on “Bing's dogbone space” belongs to the topics in three-dimensional topology motivated by the Poincaré conjecture. S Singh gives a nice synthesis of Armentrout's work. 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