Name: Torsions of 3-dimensional Manifolds By Vladimir Turaev
SKU: 9783764369118
Price: 74.39 USD
Availability: InStock

Torsions of 3-dimensional Manifolds Summary

Torsions of 3-dimensional Manifolds by Vladimir Turaev

From the reviews: This is an excellent exposition about abelian Reidemeister torsions for three-manifolds. -Zentralblatt Math

This monograph contains a wealth of information many topologists will find very handy. ...Many of the new points of view pioneered by Turaev are gradually becoming mainstream and are spreading beyond the pure topology world. This monograph is a timely and very useful addition to the scientific literature. -Mathematical Reviews

Torsions of 3-dimensional Manifolds Reviews

This is an excellent exposition about abelian Reidemeister torsions for three-manifolds.

-Zentralblatt Math

The present monograph covers in great detail the work of the author spanning almost three decades. ...[Establishing an explicit formula given a 3-manifold] is a truly remarkable feat... This monograph contains a wealth of information many topologists will find very handy. ...Many of the new points of view pioneered by Turaev are gradually becoming mainstream and are spreading beyond the pure topology world. This monograph is a timely and very useful addition to the scientific literature.

--Mathematical Reviews

I Generalities on Torsions.- I.1 Torsions of chain complexes and CW-spaces.- I.2 Combinatorial Euler structures and their torsions.- I.3 The maximal abelian torsion.- I.4 Smooth Euler structures and their torsions.- II The Torsion versus the Alexander-Fox Invariants.- II.1 The first elementary ideal.- II.2 The case b1 ? 2.- II.3 The case b1 = 1.- II.4 Extension to 3-manifolds with boundary.- II.5 The Alexander polynomials.- III The Torsion versus the Cohomology Rings.- III.1 Determinant and Pfaffian for alternate trilinear forms.- III.2 The integral cohomology ring.- III.3 Square volume forms and refined determinants.- III.4 The cohomology ring mod r.- IV The Torsion Norm.- IV.1 The torsion polytope and the torsion norm.- IV.2 Comparison with the Thurston norm.- IV.3 Proof of Theorem 2.2.- V Homology Orientations in Dimension Three.- V.1 Relative torsions of chain complexes.- V.2 Induced homology orientations.- V.3 Homology orientations and link exteriors.- V.4 Homology orientations and surgery.- VI Euler Structures on 3-manifolds.- VI.1 Gluing of smooth Euler structures and the class c.- VI.2 Euler structures on solid tori and link exteriors.- VI.3 Gluing of combinatorial Euler structures and torsions.- VII A Gluing Formula with Applications.- VII.1 A gluing formula.- VII.2 The Alexander-Conway function and surgery.- VII.3 Proof of Formula (I.4.e).- VII.4 The torsion versus the Casson-Walker-Lescop invariant.- VII.5 Examples and computations.- VIII Surgery Formulas for Torsions.- VIII.1 Two lemmas.- VIII.2 A surgery formula for ?-torsions.- VIII.3 A surgery formula for the Alexander polynomial.- VIII.4 A surgery formula for ?(M) in the case b1(M) ? 1.- VIII.5 Realization of the torsion.- IX The Torsion Function.- IX.1 The torsion function, basic Euler structures, and gluing.- IX.2 Moments of the torsion function.- IX.3 Axioms for the torsion function.- IX.4 A surgery formula for the torsion function.- IX.5 Formal expansions in Q(H) with applications.- X Torsion of Rational Homology Spheres.- X.1 The torsion and the first elementary ideal.- X.2 The torsion versus the linking form.- X.3 The torsion versus the cohomology ring mod r.- X.4 A gluing formula.- X.5 A surgery formula.- X.6 The torsion function and its moments.- XI Spinc Structures.- XI.1 Spinc structures on 3-manifolds.- XI.2 The torsion function versus the Seiberg-Witten invariants.- XI.3 Spin structures on 3-manifolds.- XII Miscellaneous.- XII.1 Torsions of connected sums.- XII.2 The torsion versus the Massey products.- XII.3 Genus estimates for ?r-surfaces.- Open Problems.

Additional information

Sku

NPB9783764369118

ISBN 13

9783764369118

ISBN 10

3764369116

Title

Torsions of 3-dimensional Manifolds by Vladimir Turaev

Author

Vladimir Turaev

Series

Progress in Mathematics

Condition

New

Binding type

Hardback

Publisher

Birkhauser Verlag AG

Year published

2002-11-21

Number of pages

196

Prizes

N/A

Cover note

Book picture is for illustrative purposes only, actual binding, cover or edition may vary.

Note

This is a new book - be the first to read this copy. With untouched pages and a perfect binding, your brand new copy is ready to be opened for the first time

Torsions of 3-dimensional Manifolds Vladimir Turaev

Torsions of 3-dimensional Manifolds by Vladimir Turaev

Summary

Torsions of 3-dimensional Manifolds Summary

Torsions of 3-dimensional Manifolds by Vladimir Turaev

Torsions of 3-dimensional Manifolds Reviews

Table of Contents

Additional information

Customer Reviews - Torsions of 3-dimensional Manifolds