Dijkgraaf-Witten Type Invariants of Seifert Surfaces in 3-Manifolds

TL;DR

This paper extends Dijkgraaf-Witten theory by incorporating defects with internal gauge symmetries on knots and Seifert surfaces, using specialized categorical data to construct invariants of 3-manifolds.

Contribution

It introduces a novel combinatorial framework for Dijkgraaf-Witten invariants that includes defects and gauge symmetries on knots and Seifert surfaces, based on new categorical data.

Findings

Develops a new combinatorial construction for invariants

Incorporates defects with gauge symmetries into the theory

Defines initial data using categories satisfying cocycle conditions

Abstract

We introduce defects, with internal gauge symmetries, on a knot and Seifert surface to a knot into the combinatorial construction of finite gauge-group Dijkgraaf-Witten theory. The appropriate initial data for the construction are certain three object categories, with coefficients satisfying a partially degenerate cocycle condition.