arXiv subjects

Marina Appiou Nikiforou

Publications and source records attributed to Marina Appiou Nikiforou.

2 recordsLinked to original sources

arXiv2002

Cocycle Knot Invariants, Quandle Extensions, and Alexander Matrices

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.

math.GT↗

arXiv2001

Extensions of Quandles and Cocycle Knot Invariants

Quandle cocycles are constructed from extensions of quandles. The theory is parallel to that of group cohomology and group extensions. An interpretation of quandle cocycle invariants as obstructions to extending knot colorings is given, and is extended to links component-wise.

math.GT↗