# Topology Seminar

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Tue., Nov. 2, 2021 3:00 p.m.
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Location: Live Stream
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**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.