Introduction to Combinatorial Torsions

ISBN-13: 9783764364038 / Angielski / Miękka / 2001 / 124 str.

Vladimir Tuarev; V. G. Turaev; V. Tuarev

Opis

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.

Recenzje

"[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

Spis treści

I Algebraic Theory of Torsions.- 1 Torsion of chain complexes.- 2 Computation of the torsion.- 3 Generalizations and functoriality of the torsion.- 4 Homological computation of the torsion.- II Topological Theory of Torsions.- 5 Basics of algebraic topology.- 6 The Reidemeister—Franz torsion.- 7 The Whitehead torsion.- 8 Simple homotopy equivalences.- 9 Reidemeister torsions and homotopy equivalences.- 10 The torsion of lens spaces.- 11 Milnor’s torsion and Alexander’s function.- 12 Group rings of finitely generated abelian groups.- 13 The maximal abelian torsion.- 14 Torsions of manifolds.- 15 Links.- 16 The Fox Differential Calculus.- 17 Computing ?(M3) from the Alexander polynomial of links.- III Refined Torsions.- 18 The sign-refined torsion.- 19 The Conway link function.- 20 Euler structures.- 21 Torsion versus Seiberg—Witten invariants.- References.