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Article Dans Une Revue Algebr.Geom.Topol. Année : 2023

Two-Dimensional Extended Homotopy Field Theories

Résumé

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.

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Dates et versions

hal-03171493 , version 1 (17-03-2021)

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Citer

Kursat Sozer. Two-Dimensional Extended Homotopy Field Theories. Algebr.Geom.Topol., 2023, 23 (9), pp.3909-3996. ⟨10.2140/agt.2023.23.3909⟩. ⟨hal-03171493⟩
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