Two-Dimensional Extended Homotopy Field Theories

Abstract

We give another definition of two-dimensional extended homotopy field theories (E-HFTs) with aspherical targets and classify them. When the target of E-HFT is chosen to be a $K(G,1)$-space, we classify E-HFTs 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 $(G\times SO(2))$-structured cobordism hypothesis due to Lurie.

Version 2 with 61 pages and 36 figures; the organization of the sections is changed and the arguments are improved in light of the referee's comments and suggestions. To appear in Algebraic & Geometry Topology

References in corpus (2)

• Orientation twisted homotopy field theories and twisted unoriented Dijkgraaf-Witten theory
• 't Hooft anomalies of discrete gauge theories and non-abelian group cohomology

Cited by in corpus (1)

• Reflection Structures and Spin Statistics in Low Dimensions