Algebraic Structure of Knot Modules

✍ Scribed by Jerome P. Levine (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1980
• Tongue: English
• Leaves: 141
• Series: Lecture Notes in Mathematics 772
• Edition: 1
• Category: Library

✦ Table of Contents

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

✦ Subjects

Algebraic Topology