Algebraic Structure of Knot Modules

Inhaltsverzeichnis

• The derived exact sequences.
• Finite modules.
• Realization of finite modules.
• ? i of finite modules.
• Product structure on finite modules.
• Classification of derived product structure.
• Rational invariants.
• Z-torsion-free modules.
• ?-only torsion.
• Statement of realization theorem.
• Inductive construction of derived sequences.
• Inductive recovery of derived sequences.
• Homogeneous and elementary modules.
• Realization of elementary modules.
• Classification of elementary modules.
• Completion of proof.
• Classification of ?-primary modules.
• Classification fails in degree 4.
• Product structure on ?-primary modules.
• Classification of product structure.
• Realization of product structure on homogeneous modules.
• Product structure on semi-homogeneous modules.
• A non-semi-homogeneous module.
• Rational classification of product structure.
• Non-singular lattices over a Dedekind domain.
• Norm criterion for a non-singular lattice.
• Dedekind criterion: p-adic reduction.
• A computable Dedekind criterion.
• Computation of low-degree cases.
• Determination of ideal class group.
• The quqdratic symetric case.