Categorical Groups, Knots and Knotted Surfaces

Abstract

We define a knot invariant and a 2-knot invariant from any finite categorical group. We calculate an explicit example for the Spun Trefoil.

40 pages, lots of figures. Second version: Added example and discussion, clarification of the fact that the maps associated with Reidemeister Moves are well defined

References in corpus (2)

• Khovanov's homology for tangles and cobordisms
• Observables in the Turaev-Viro and Crane-Yetter models

Cited by in corpus (7)

• From gauge to higher gauge models of topological phases
• Topological phases from higher gauge symmetry in 3+1D
• The Fundamental Crossed Module of the Complement of a Knotted Surface
• Link invariants from finite categorical groups and braided crossed modules
• On 2-Dimensional Homotopy Invariants of Complements of Knotted Surfaces
• Link invariants from finite categorical groups
• Crossed modules of racks