On higher holonomy invariants in higher gauge theory II

TL;DR

This paper develops a framework for higher holonomy invariants in strict higher gauge theory, introducing a trace over crossed modules to produce surface knot invariants, with applications to higher Chern--Simons theory.

Contribution

It defines a trace over crossed modules for higher gauge theory and demonstrates its use in constructing surface knot invariants, advancing the mathematical understanding of higher holonomies.

Findings

Defined a trace over crossed modules for higher gauge theory

Constructed surface knot invariants from 2-holonomies

Connected properties of the trace with quandle crossed modules

Abstract

This is the second of a series of two technical papers devoted to the analysis of holonomy invariants in strict higher gauge theory with end applications in higher Chern--Simons theory. We provide a definition of trace over a crossed module such to yield surface knot invariants upon application to 2-holonomies. We show further that the properties of the trace are best described using the theory quandle crossed modules.