Abstract
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We give another definition of
–dimensional
extended homotopy field theories (EHFTs) with aspherical targets
and classify them. When the target of EHFT is chosen to be a
–space,
we classify EHFTs taking values in the symmetric monoidal bicategory
of algebras, bimodules, and bimodule maps by certain Frobenius
–algebras called
quasibiangular
–algebras.
As an application, for any discrete group
, we verify a special
case of the
–structured
cobordism hypothesis due to Lurie.
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Keywords
HQFTs, extended TQFTs
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Mathematical Subject Classification 2010
Primary: 57R56
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Publication
Received: 11 September 2019
Revised: 5 January 2021
Accepted: 9 February 2021
Published: 23 November 2023
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