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Torsions of 3-dimensional Manifolds (Progress in Mathematics) [Hardcover]

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Item description for Torsions of 3-dimensional Manifolds (Progress in Mathematics) by V. Turaev...

The book is concerned with one of the most interesting and important topological invariants of 3-dimensional manifolds based on an original idea of Kurt Reidemeister (1935). This invariant, called the maximal abelian torsion, was introduced by the author in 1976. The purpose of the book is to give a systematic exposition of the theory of maximal abelian torsions of 3-manifolds. Apart from publication in scientific journals, many results are recent and appear here for the first time. Topological properties of the torsion are the main focus. This includes a detailed description of relations between the torsion and the Alexander-Fox invariants of the fundamental group. The torsion is shown to be related to the cohomology ring of the manifold and to the linking form. The reader will also find a definition of the torsion norm on the 2-homology of a 3-manifold, and a comparison with the classical Thurston norm. A surgery formula for the torsion is provided which allows to compute it explicitly from a surgery presentation of the manifold. As a special case, this gives a surgery formula for the Alexander polynomial of 3-manifolds. Treated in detail are a number of relevant notions including homology orientations, Euler structures, and Spinc structures on 3-manifolds. Relations between the torsion and the Seiberg-Witten invariants in dimension 3 are briefly discussed. Students and researchers with basic background in algebraic topology and low-dimensional topology will benefit from this monograph. Previous knowledge of the theory of torsions is not required. Numerous exercises and historical remarks as well as a collection of open problems complete the exposition.

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Item Specifications...

Pages   196
Est. Packaging Dimensions:   Length: 9.1" Width: 6.3" Height: 0.7"
Weight:   1.05 lbs.
Binding  Hardcover
Release Date   Jan 31, 2003
Publisher   Birkhäuser Basel
ISBN  3764369116  
ISBN13  9783764369118  

Availability  136 units.
Availability accurate as of Oct 24, 2016 08:17.
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1Books > Special Features > New & Used Textbooks > Sciences > Mathematics > Geometry
2Books > Subjects > Medicine > General
3Books > Subjects > Professional & Technical > Professional Science > Mathematics > Geometry & Topology > General Geometry
4Books > Subjects > Professional & Technical > Professional Science > Mathematics > Geometry & Topology > Topology
5Books > Subjects > Professional & Technical > Professional Science > Mathematics > Mathematical Analysis
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7Books > Subjects > Science > Mathematics > General
8Books > Subjects > Science > Mathematics > Geometry & Topology > General Geometry
9Books > Subjects > Science > Mathematics > Geometry & Topology > Topology
10Books > Subjects > Science > Mathematics > Mathematical Analysis

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