Two-dimensional Extended Homotopy Quantum Field Theories

Abstract

We define two-dimensional extended homotopy quantum field theories (E-HQFTs) with aspherical targets and classify them. When the target of E-HQFT is chosen to be a K(G,1)-space, we classify oriented E-HQFTs taking values in the symmetric monoidal bicategory of algebras, bimodules, and bimodule maps by certain Frobenius G-algebras called quasi-biangular G-algebras. As an application, for any discrete group G, we verify a special case of the (G x SO(2))-structured cobordism hypothesis due to Lurie.