Classification of Two-Dimensional Homotopy Quantum Field Theories

Abstract

In [Remarks on 2-dimensional HQFT's] Staic and Turaev assigned a generalised Frobenius algebra - the twisted Frobenius algebra to two-dimensional Homotopy Quantum Field Theories, and showed that two HQFTs are isomorphic if and only if their assigned algebras are equivalent. We define a symmetric monoidal functor version of Turaev's definition and extend this result to an equivalence of categories. During this discussion we also review standard topological quantum field theory as well as extended topological quantum field theory. Show more