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SUMMARY:Mehmet Akif Erdal (Yeditepe Universitesi)
DTSTART:20211101T133000Z
DTEND:20211101T143000Z
DTSTAMP:20260422T135430Z
UID:BilTop/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BilTop/32/">
 An Elmendorf-Piacenza type Theorem for Actions of Monoids</a>\nby Mehmet A
 kif Erdal (Yeditepe Universitesi) as part of Bilkent Topology Seminar\n\nL
 ecture held in SB-Z11.\n\nAbstract\nIn this talk I will describe a homotop
 y theory for actions of monoids that is built by analyzing their ``reversi
 ble 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 mo
 del 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 st
 ructure is Quillen equivalent to the projective model structure on the cat
 egory of contravariant $\\mathbf{O}(M)$-diagrams of spaces\, where $\\math
 bf{O}(M)$ 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 $M$-equivaria
 nt maps. Finally\, if time permits\, I will state some applications.\n
LOCATION:https://researchseminars.org/talk/BilTop/32/
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