Online Talk

Topological Hochschild homology, an invariant of ring spectra, is the realization of a cyclic object defined using Connes' cyclic category and it carries an action of the circle. Real topological Hochschild homology, an invariant of ring spectra with involution, is the realization of a dihedral object defined using the dihedral category and it carries an action of O(2). In this talk, we describe a simultaneous generalization of these constructions, a topological version of homology which takes as input rings with twisted group action, which generalize rings with involution. A new example of interest of this construction is quaternionic topological Hochschild homology, which carries a Pin(2)-action. This is joint work with Gabriel Angelini-Knoll and Maximilien Péroux.