MATH Semineri: “An Elmendorf-Piacenza type Theorem for Actions of Monoids”, Mehmet Akif Erdal, 16:30 1 Kasım (EN)

An Elmendorf-Piacenza type Theorem for Actions of Monoids
Mehmet Akif Erdal
(Yeditepe Universitesi)

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 $Nleq M$. 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 $Mtimes_N G(N)/H$ for each $Nleq M$ and $Hleq G(N)$ and morphisms are $M$-equivariant maps. Finally, if time permits, I will state some applications.

Date: 1 November, 2021
Time: 16:30 UTC+3
Place: Zoom
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