Generalizations of Quandle Cocycle Invariants and Alexander Modules from Quandle Modules

TL;DR

This paper reviews recent advances in quandle cocycle invariants and Alexander modules, highlighting their applications to classical knots and knotted surfaces, and discusses generalizations of these algebraic invariants.

Contribution

It provides a summary of new generalizations of quandle cocycle invariants and Alexander modules, expanding their applicability in knot theory.

Findings

Enhanced invariants for classical knots and surfaces

New algebraic structures generalizing existing invariants

Applications demonstrating the effectiveness of these invariants

Abstract

This paper is a brief overview of some of our recent results in collaboration with other authors. The cocycle invariants of classical knots and knotted surfaces are summarized, and some applications are presented.