# A cellular topological field theory

## TL;DR

This paper constructs a cellular topological quantum field theory, specifically cellular BF theory, that is invariant under subdivision, satisfies the quantum master equation, and obeys gluing formulas, advancing the mathematical understanding of topological invariants.

## Contribution

It introduces a cellular construction of BF theory on cobordisms with cellular decompositions, providing invariance, quantum consistency, and gluing properties.

## Key findings

- Partition functions are subdivision invariant.
- The theory satisfies a version of the quantum master equation.
- It obeys Atiyah-Segal-type gluing formulas.

## Abstract

We present a construction of cellular BF theory (in both abelian and non-abelian variants) on cobordisms equipped with cellular decompositions. Partition functions of this theory are invariant under subdivisions, satisfy a version of the quantum master equation, and satisfy Atiyah-Segal-type gluing formula with respect to composition of cobordisms.