Homologically Twisted Invariants Related to (2+1)- and (3+1)-Dimensional State-Sum Topological Quantum Field Theories

TL;DR

This paper constructs new topological invariants related to (2+1) and (3+1)-dimensional state-sum TQFTs, inspired by physical insights connecting BF theory and Donaldson polynomials, and dependent on cohomology classes.

Contribution

It introduces homologically twisted invariants for state-sum TQFTs, extending existing invariants like Turaev/Viro and Crane/Yetter with cohomology class dependence.

Findings

Constructed new homologically twisted invariants for TQFTs.

Extended the scope of Turaev/Viro and Crane/Yetter invariants.

Provided a framework linking physical theories to topological invariants.

Abstract

Motivated by suggestions of Paolo Cotta-Ramusino's work at the physical level of rigor relating BF theory to the Donaldson polynomials, we provide a construction applicable to the Turaev/Viro and Crane/Yetter invariants of *a priori* finer invariants dependent on a choice of (co)homology class on the manifold