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SUMMARY:Cobordism\, spin structures\, and profinite completions - Andrew N
 g\, University of Bonn
DTSTART:20260220T160000Z
DTEND:20260220T170000Z
UID:TALK242935@talks.cam.ac.uk
CONTACT:Julian Wykowski
DESCRIPTION:A surprising theorem of Wilton-Zalesski says that the geometri
 c structure of a geometric 3-manifold can be determined purely from the se
 t of finite quotients of its fundamental group\, or equivalently the profi
 nite completion. This raises the question of what other geometric and topo
 logical invariants can be seen in the profinite completion. Recall that th
 e Stiefel-Whitney classes of a manifold are characteristic classes in mod 
 2 cohomology that detect important properties\, such as orientability\, th
 e unoriented bordism class\, and admitting a spin structure.  In joint wor
 k with Sam Hughes\, we show that for compact aspherical manifolds with fun
 damental group that is good in the sense of Serre\, these characteristic c
 lasses are invariants of the profinite completion. This raises the possibi
 lity of applications to questions of profinite rigidity\, and as a sample 
 application we are able to show the profinite rigidity of the fundamental 
 group of a flat 6-manifold.
LOCATION:MR13
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