Remarks on 2-dimensional HQFT's

TL;DR

This paper introduces twisted Frobenius algebras as the algebraic foundation for 2-dimensional Homotopy Quantum Field Theories with arbitrary target spaces, extending previous results to more general settings.

Contribution

It generalizes the algebraic framework of 2D HQFTs to include arbitrary target spaces using twisted Frobenius algebras, broadening the scope of prior work.

Findings

Defined twisted Frobenius algebras for HQFTs

Extended previous results to non-simply-connected targets

Provided a new algebraic formalism for 2D HQFTs

Abstract

We introduce and study algebraic structures underlying 2-dimensional Homotopy Quantum Field Theories (HQFTs) with arbitrary target spaces. These algebraic structures are formalized in the notion of a twisted Frobenius algebra. Our work generalizes results of Brightwell, Turner, and the second author on 2-dimensional HQFTs with simply-connected or aspherical targets.