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Introduction to Combinatorial Torsions : Lectures in Mathematics Eth Zurich - Vladimir Turaev

Introduction to Combinatorial Torsions

Lectures in Mathematics Eth Zurich

Paperback Published: 2001
ISBN: 9783764364038
Number Of Pages: 124

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This book is an introduction to combinatorial torsions of cellular spaces and manifolds with special emphasis on torsions of 3-dimensional manifolds. The first two chapters cover the algebraic foundations of the theory of torsions and various topological constructions of torsions. The third and last chapter deals with so-called refined torsions and the related additional structures. The book includes the necessary amount of standard background material to be accessible to the beginner.

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"[The book] contains much of the needed background material in topology and algebra...Concering the considerable material it covers, [the book] is very well-written and readable."

--Zentralblatt Math

Introduction
Algebraic Theory of Torsions
Torsion of chain complexesp. 1
Computation of the torsionp. 7
Generalizations and functoriality of the torsionp. 12
Homological computation of the torsionp. 16
Topological Theory of Torsions
Basics of algebraic topologyp. 23
The Reidemeister-Franz torsionp. 30
The Whitehead torsionp. 35
Simple homotopy equivalencesp. 40
Reidemeister torsions and homotopy equivalencesp. 43
The torsion of lens spacesp. 44
Milnor's torsion and Alexander's functionp. 51
Group rings of finitely generated abelian groupsp. 58
The maximal abelian torsionp. 64
Torsions of manifoldsp. 69
Linksp. 81
The Fox Differential Calculusp. 83
Computing [tau](M[superscript 3]) from the Alexander polynomial of linksp. 92
Refined Torsions
The sign-refined torsionp. 97
The Conway link functionp. 102
Euler structuresp. 108
Torsion versus Seiberg-Witten invariantsp. 112
Referencesp. 117
Indexp. 121
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783764364038
ISBN-10: 3764364033
Series: Lectures in Mathematics Eth Zurich
Audience: General
Format: Paperback
Language: English
Number Of Pages: 124
Published: 2001
Publisher: Birkhauser Verlag AG
Country of Publication: CH
Dimensions (cm): 23.98 x 17.02  x 0.99
Weight (kg): 0.26

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