Evaluating the Crane-Yetter Invariant

TL;DR

This paper derives an explicit combinatorial formula for the Crane-Yetter invariant of 4-manifolds, linking it to the signature of the manifold and potential physical theories.

Contribution

It provides the first explicit formula for the Crane-Yetter invariant, enabling computation from local triangulation data and connecting it to physical models.

Findings

Explicit formula for the Crane-Yetter invariant

Combinatorial formula for 4-manifold signature

Potential applications in topological quantum field theory

Abstract

We provide an explicit formula for the invariant of 4-manifolds introduced by Crane and Yetter (in hep-th 9301062). A consequence of our result is the existence of a combinatorial formula for the signature of a 4-manifold in terms of local data from a triangulation. Potential physical applications of our result exist in light of the fact that the Crane-Yetter invariant is a rigorous version of ideas of Ooguri on B wedge F theory.