Two-dimensional extended homotopy field theories

Sözer, Kürşat

doi:10.2140/agt.2023.23.3909

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Two-dimensional extended homotopy field theories

Kürşat Sözer

Algebraic & Geometric Topology 23 (2023) 3909–3996

DOI: 10.2140/agt.2023.23.3909

Abstract

We give another definition of $2$ –dimensional extended homotopy field theories (EHFTs) with aspherical targets and classify them. When the target of EHFT is chosen to be a $K (G, 1)$ –space, we classify EHFTs taking values in the symmetric monoidal bicategory of algebras, bimodules, and bimodule maps by certain Frobenius $G$ –algebras called quasibiangular $G$ –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.

Keywords

HQFTs, extended TQFTs

Mathematical Subject Classification 2010

Primary: 57R56

References

Publication

Received: 11 September 2019

Revised: 5 January 2021

Accepted: 9 February 2021

Published: 23 November 2023

Authors

Kürşat Sözer
Le laboratoire de mathématiques Paul Painlevé Université de Lille Lille France

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Volume 23, issue 9 (2023)