Online Talk

Equivariant Loday constructions are a means for providing geometric  interpretations of equivariant homology theories such as topological Real Hochschild homology. For the family of dihedral groups Angelini-Knoll, Gerhardt and Hill defined Real $D_{2m}$-Hochschild homology groups for discrete $E_\sigma$-rings. In joint work with Ayelet Lindenstrauss and Foling Zou we show that these have an interpretation as the homotopy  groups of an equivariant Loday construction where we consider a $D_{2m}$-action on the $1$-skeleton of a regular $2m$-gon. To that end we need to generalize equivariant Loday constructions so that the Tambara functor only needs to take into account the isotropy subgroups of the $G$-simplicial set. If time permits, we will also present a family of examples related to the symmetric group actions on permutohedra.