Wilson Surfaces for Surface Knots
arXiv:1903.02853
Abstract
Holonomy invariants in strict higher gauge theory have been studied in depth, aiming to applications to higher Chern-Simons theory. For a flat 2-connection, the holonomy of surface knots of arbitrary genus has been defined and its covariance properties under 1-gauge transformation and change of base data have been determined. Using quandle theory, a definition of trace over a crossed module has been given that yields surface knot invariants upon application to 2-holonomies.
15 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 2018