Cocycle Knot Invariants, Quandle Extensions, and Alexander Matrices

J. Scott Carter; Angela Harris; Marina Appiou Nikiforou; Masahico Saito

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Cocycle Knot Invariants, Quandle Extensions, and Alexander Matrices

J. Scott Carter·Angela Harris·Marina Appiou Nikiforou·Masahico Saito

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Abstract

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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J. Scott Carter, Angela Harris, Marina Appiou Nikiforou, Masahico Saito. 2002-04-10. Cocycle Knot Invariants, Quandle Extensions, and Alexander Matrices. https://arxiv.org/abs/math/0204113

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