
Topology Seminar
Tue., Nov. 2, 2021 3:00 p.m.
Location: Live Stream
Speaker: Maximilien Péroux, University of Pennsylvania
Title: Equivariant variations of topological Hochschild homology
Zoom: https://uregina-ca.zoom.us/j/99127226830?pwd=bnFQR1R3UUdyWUxqSS9JMExMRlZwZz09
Abstract:
Topological Hochschild homology (THH) is an important variant for ring spectra. It is built as a geometric realization of a cyclic bar construction. It is endowed with an action of circle. This is because it is a geometric realization of a cyclic object. The simplex category factors through Connes’ category Λ. Similarly, real topological Hochschild homology (THR) for ring spectra with anti-involution is endowed with a O(2)-action. Here instead of the cyclic category Λ, we use the dihedral category Ξ.
From work in progress with Gabe Angelini-Knoll and Mona Merling, I present a generalization of Λ and Ξ called crossed simplicial groups, introduced by Fiedorowicz and Loday. To each crossed simplical group G, I define THG, an equivariant analogue of THH. Its input is a ring spectrum with a twisted group action. THG is an algebraic invariant endowed with different action and cyclotomic structure, and generalizes THH and THR.