An Elmendorf-Piacenza type Theorem for Actions of Monoids

Abstract: In this talk I will describe a homotopy theory for actions of monoids that is built by analyzing their ``reversible parts". Let $M$ be a monoid and $G(M)$ be its group completion. I will show that the category of $M$-spaces and $M$-equivariant maps admits a model structure in which weak equivalences and fibrations are determined by the standard equivariant homotopy theory of $G(N)$-spaces for each $N\leq M$. Then, I will show that under certain conditions on $M$ this model structure is Quillen equivalent to the projective model structure on the category of contravariant $\mathbf{O}(M)$-diagrams of spaces, where $\mathbf{O}(M)$ is the category whose objects are induced orbits $M\times_N G(N)/H$ for each $N\leq M$ and $H\leq G(N)$ and morphisms are $M$-equivariant maps. Finally, if time permits, I will state some applications.

algebraic topologycategory theorygroup theoryK-theory and homology

Audience: researchers in the topic

Cihan Okay

Series comments: Contact the organizer to get access to Zoom.

Recordings of talks available at www.youtube.com/channel/UCLrmyGpqxyeVpTcA1b5HcMw/videos