Author Description

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