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SUMMARY:Detecting exotic smooth structures in diffeomorphism groups - Manu
 el Krannich\, Cambridge
DTSTART:20181114T160000Z
DTEND:20181114T170000Z
UID:TALK107647@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:The well-studied inertia group of a closed manifold M captures
  the behaviour of the diffeomorphism type of M when changing the smooth st
 ructure of M on a codimension zero disc\; that is\, when taking the connec
 ted sum M#S with an exotic sphere S. Instead of comparing their diffeomorp
 hism types\, one might try to compare the group of diffeomorphisms of M an
 d M#S. However\, homotopically\, the space of diffeomorphisms Diff(M) deco
 mposes as a twisted product whose factors are insensitive to replacing M w
 ith M#S. This suggests that it is hard to detect the possible exotic natur
 e of M#S by means of homotopical properties of its group of diffeomorphism
 s. Using recent progress in manifold theory by Galatius and Randal-William
 s\, together with computations in stable homotopy theory\, I will discuss 
 results on the behaviour of the cohomology of BDiff(M) when replacing M wi
 th M#S.
LOCATION:MR13
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