Torsions of 3-dimensional Manifolds
des. 2012 · Progress in Mathematics Bók 208 · Birkhäuser
Rafbók
196
Síður
reportEinkunnir og umsagnir eru ekki staðfestar Nánar
Um þessa rafbók
Three-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).
Gefa þessari rafbók einkunn.
Segðu okkur hvað þér finnst.
Upplýsingar um lestur
Snjallsímar og spjaldtölvur
Settu upp forritið Google Play Books fyrir Android og iPad/iPhone. Það samstillist sjálfkrafa við reikninginn þinn og gerir þér kleift að lesa með eða án nettengingar hvar sem þú ert.
Fartölvur og tölvur
Hægt er að hlusta á hljóðbækur sem keyptar eru í Google Play í vafranum í tölvunni.
Lesbretti og önnur tæki
Til að lesa af lesbrettum eins og Kobo-lesbrettum þarftu að hlaða niður skrá og flytja hana yfir í tækið þitt. Fylgdu nákvæmum leiðbeiningum hjálparmiðstöðvar til að flytja skrár yfir í studd lesbretti.
