Cocycle Knot Invariants, Quandle Extensions, and Alexander Matrices

Details Cocycle Knot Invariants, Quandle Extensions, and Alexander Matrices Cocycle Knot Invariants, Quandle Extensions, and Alexander Matrices

2002-04-10

arxiv.org/abs/math/0204113v1

Mathematics

Geometric Topology

24 pages, 10 figures. submitted to the Kyoto conf. proceedings

Scientific paper

The theory of quandle (co)homology and cocycle knot invariants is rapidly being developed. We begin with a summary of these recent advances. One such advance is the notion of a dynamical cocycle. We show how dynamical cocycles can be used to color knotted surfaces that are obtained from classical knots by twist-spinning. We also demonstrate relations between cocycle invariants and Alexander matrices.

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