{"product_id":"torsions-of-3-dimensional-manifolds-paperback","title":"Torsions of 3-Dimensional Manifolds - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eVladimir Turaev\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003eThree-dimensional topology includes two vast domains: the study of geometric structures on 3-manifolds and the study of topological invariants of 3-manifolds, knots, etc. This book belongs to the second domain. We shall study an invariant called the maximal abelian torsion and denoted T. It is defined for a compact smooth (or piecewise-linear) manifold of any dimension and, more generally, for an arbitrary finite CW-complex X. The torsion T(X) is an element of a certain extension of the group ring Z[Hl(X)]. The torsion T can be naturally considered in the framework of simple homotopy theory. In particular, it is invariant under simple homotopy equivalences and can distinguish homotopy equivalent but non- homeomorphic CW-spaces and manifolds, for instance, lens spaces. The torsion T can be used also to distinguish orientations and so-called Euler structures. Our interest in the torsion T is due to a particular role which it plays in three-dimensional topology. First of all, it is intimately related to a number of fundamental topological invariants of 3-manifolds. The torsion T(M) of a closed oriented 3-manifold M dominates (determines) the first elementary ideal of 7fl (M) and the Alexander polynomial of 7fl (M). The torsion T(M) is closely related to the cohomology rings of M with coefficients in Z and ZjrZ (r; 2). It is also related to the linking form on Tors Hi (M), to the Massey products in the cohomology of M, and to the Thurston norm on H2(M).\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 196\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.45 x 9.21 x 6.14 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e October 24, 2012\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":52704859062579,"sku":"9783034893985","price":96.08,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0300\/5595\/6612\/files\/YnphU2wyRGFCWDBMdWR5aUZDUlZkQT09.webp?v=1763366289","url":"https:\/\/www.vysn.com\/en-ca\/products\/torsions-of-3-dimensional-manifolds-paperback","provider":"VYSN","version":"1.0","type":"link"}