Remarks on 2-dimensional HQFT's

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.

22 pages, 14 figures. In this version we added a detailed proof for Theorem 3.3 and made some minor corrections.

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