Algebraic Structure of Knot Modules

Description

The derived exact sequences....Pages 1-4 Finite modules....Pages 4-6 Realization of finite modules....Pages 6-8 Δ i of finite modules....Pages 8-9 Product structure on finite modules....Pages 9-16 Classification of derived product structure....Pages 16-18 Rational invariants....Pages 18-20 Z-torsion-free modules....Pages 20-21 Π-only torsion....Pages 21-23 Statement of realization theorem....Pages 23-24 Inductive construction of derived sequences....Pages 24-26 Inductive recovery of derived sequences....Pages 26-32 Homogeneous and elementary modules....Pages 32-34 Realization of elementary modules....Pages 34-36 Classification of elementary modules....Pages 36-39 Completion of proof....Pages 39-40 Classification of Π-primary modules....Pages 40-46 Classification fails in degree 4....Pages 46-47 Product structure on Π-primary modules....Pages 48-53 Classification of product structure....Pages 53-59 Realization of product structure on homogeneous modules....Pages 59-67 Product structure on semi-homogeneous modules....Pages 68-70 A non-semi-homogeneous module....Pages 70-75 Rational classification of product structure....Pages 75-85 Non-singular lattices over a Dedekind domain....Pages 85-88 Norm criterion for a non-singular lattice....Pages 88-90 Dedekind criterion: p-adic reduction....Pages 90-92 A computable Dedekind criterion....Pages 92-94 Computation of low-degree cases....Pages 95-95 Determination of ideal class group....Pages 96-98 The quqdratic symetric case....Pages 98-101