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SUMMARY:Topological homology of rings with twisted group action - Mona Mer
 ling (University of Pennsylvania)
DTSTART:20250513T104500Z
DTEND:20250513T114500Z
UID:TALK230527@talks.cam.ac.uk
DESCRIPTION:Topological Hochschild homology\, an invariant of ring spectra
 \, is the realization of a cyclic object defined using Connes' cyclic cate
 gory and it carries an&nbsp\;action of the circle. Real topological Hochsc
 hild homology\, an invariant of ring spectra with involution\, is the real
 ization of a dihedral object defined using the dihedral category and it ca
 rries an action of O(2). In this talk\, we describe&nbsp\;a simultaneous g
 eneralization of these constructions\, a topological version of homology w
 hich takes as input rings with twisted group action\, which generalize rin
 gs with involution. A new example of interest of this construction is quat
 ernionic topological Hochschild homology\, which carries a Pin(2)-action. 
 This is joint work with Gabriel Angelini-Knoll and Maximilien P&eacute\;ro
 ux.
LOCATION:Seminar Room 1\, Newton Institute
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