| Introduction 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 Q-torsions Ⅷ.3 A surgery formula for the Alexander polynomial Ⅷ.4 A surgery formula for T(M) in the case bl(M)≥1 Ⅷ.5 Realization of the torsion Ⅸ The Torsion Function Ⅸ1 The torsion function, basic Euler structures, and gluing Ⅸ2 Moments of the torsion function Ⅸ3 AⅪoms for the torsion function Ⅸ4 A surgery formula for the torsion function Ⅸ5 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 eohomology ring rood r Ⅹ.4 A gluing formula Ⅹ.5 A surgery formula Ⅹ.6 The torsion function and its moments Ⅺ Spin c Structures Ⅺ.1 Spin c 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 Zr-surfaces Open Problems Bibliography Index |
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