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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:Detecting exotic smooth structures in diffeomorphi
sm groups - Manuel Krannich\, Cambridge
DTSTART;TZID=Europe/London:20181114T160000
DTEND;TZID=Europe/London:20181114T170000
UID:TALK107647AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/107647
DESCRIPTION:The well-studied inertia group of a closed manifol
d M captures the behaviour of the diffeomorphism t
ype of M when changing the smooth structure of M o
n a codimension zero disc\; that is\, when taking
the connected sum M#S with an exotic sphere S. Ins
tead of comparing their diffeomorphism types\, one
might try to compare the group of diffeomorphisms
of M and M#S. However\, homotopically\, the space
of diffeomorphisms Diff(M) decomposes as a twiste
d product whose factors are insensitive to replaci
ng M with M#S. This suggests that it is hard to de
tect the possible exotic nature of M#S by means of
homotopical properties of its group of diffeomorp
hisms. Using recent progress in manifold theory by
Galatius and Randal-Williams\, together with comp
utations in stable homotopy theory\, I will discus
s results on the behaviour of the cohomology of BD
iff(M) when replacing M with M#S.
LOCATION:MR13
CONTACT:Ivan Smith
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