Categorical Center of Higher Genera and 4D Factorization Homology

TL;DR

This paper computes the Crane-Yetter 4D topological quantum field theory for punctured surfaces, introducing the categorical center of higher genera, which generalizes quantum invariants of knots and 3-manifolds.

Contribution

It provides explicit calculations of the Crane-Yetter theory for all punctured surfaces, extending the understanding of 4D TQFTs and their relation to lower-dimensional invariants.

Findings

Categorical center of higher genera constructed for punctured surfaces

Explicit computations of Crane-Yetter 4D TQFT for these surfaces

Connections to quantum invariants like Jones polynomials

Abstract

Many quantum invariants of knots and 3-manifolds (e.g. Jones polynomials) are special cases of the Witten-Reshetikhin-Turaev 3D TQFT. The latter is in turn a part of a larger theory - the Crane-Yetter 4D TQFT. In this work, we compute the Crane-Yetter theory for all (smooth and oriented) surfaces with at least one puncture. The results in general are constructed and called the categorical center of higher genera.