2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63757The 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.24 pages, 10 figures. submitted to the Kyoto conf. proceedingsGeometric TopologyQuantum Algebra57M25; 57Q45; 57M05; 55N99; 55N22text