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SUMMARY:Oscar Randal-Williams (University of Oxford)
DTSTART:20200914T203000Z
DTEND:20200914T213000Z
DTSTAMP:20260423T004731Z
UID:MITTop/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITTop/20/">
 Diffeomorphisms of discs</a>\nby Oscar Randal-Williams (University of Oxfo
 rd) as part of MIT topology seminar\n\n\nAbstract\nIn dimensions $n \\neq 
 4$ the difference between groups of diffeomorphisms and of\nhomeomorphisms
  of an $n$-manifold $M$ is governed by an $h$-principle\, meaning that it 
 reduces to understanding these groups for $M=\\mathbb{R}^n$. The group of 
 diffeomorphisms is simple\, by linearising it is equivalent to $O(n)$\, bu
 t the group $Top(n)$ of homeomorphisms of $\\mathbb{R}^n$ has little struc
 ture and is difficult to grasp. It is profitable to instead consider the $
 n$-disc $M=D^n$\, because the group of homeomorphisms of a disc (fixing th
 e boundary) is\ncontractible by Alexander's trick: this removes homeomorph
 isms from the picture\nentirely\, and makes the problem one purely within 
 differential topology. I will\nexplain some of the history of this problem
 \, as well as recent work with A. Kupers in this direction.\n
LOCATION:https://researchseminars.org/talk/MITTop/20/
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