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Two-dimensional extended homotopy field theories

Kürşat Sözer

Algebraic & Geometric Topology 23 (2023) 3909–3996
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×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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