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SUMMARY:Spaces of diffeomorphisms and embeddings of high-dimensional manif
 olds - Samuel Muñoz-Echániz\, University of Cambridge 
DTSTART:20231006T144000Z
DTEND:20231006T154000Z
UID:TALK204286@talks.cam.ac.uk
CONTACT:Alexis Marchand
DESCRIPTION:The homotopy type of the diffeomorphism group of a manifold is
  an object of great interest in algebraic and geometric topology. In this 
 talk I will survey the “surgery-pseudoisotopy program” to study these 
 objects for high-dimensional manifolds. In doing so\, we will learn a bit 
 about surgery theory\, h-cobordisms and algebraic K-theory. We will end up
  deducing the computation of the rational homotopy groups of the diffeomor
 phism group of a disc in a range depending on its dimension.\n\nIf time pe
 rmits (which I doubt)\, I will explain how the relative version of this pr
 ogram can be used to fully describe the homotopy type (localised away from
  2) of spaces of long knots in high-dimensions up to a surprisingly big ra
 nge.
LOCATION:MR13
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