A Survey of Quantum Enhancements

Abstract

In this short survey article we collect the current state of the art in the nascent field of quantum enhancements, a type of knot invariant defined by collecting values of quantum invariants of knots with colorings by various algebraic objects over the set of such colorings. This class of invariants includes classical skein invariants and quandle and biquandle cocycle invariants as well as new invariants.