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SUMMARY:Renee Hoekzema (Univ. Oxford)
DTSTART:20210122T170000Z
DTEND:20210122T180000Z
DTSTAMP:20260423T024611Z
UID:TQFT/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TQFT/26/">Ma
 nifolds with odd Euler characteristic and higher orientability</a>\nby Ren
 ee Hoekzema (Univ. Oxford) as part of Topological Quantum Field Theory Clu
 b (IST\, Lisbon)\n\n\nAbstract\nOrientable manifolds have even Euler chara
 cteristic unless the dimension is a multiple of 4. I give a generalisation
  of this theorem: $k$-orientable manifolds have even Euler characteristic 
 (and in fact vanishing top Wu class)\, unless their dimension is $2^{k+1}m
 $ for some integer $m$. Here we call a manifold $k$-orientable if the $i^{
 \\rm th}$ Stiefel-Whitney class vanishes for all $0 < i < 2^k$. This theor
 em is strict for $k=0\,1\,2\,3$\, but whether there exist 4-orientable man
 ifolds with an odd Euler characteristic is a new open question. Such manif
 olds would have dimensions that are a multiple of 32. I discuss manifolds 
 of dimension high powers of 2 and present the results of calculations on t
 he cohomology of the second Rosenfeld plane\, a special 64-dimensional man
 ifold with odd Euler characteristic.\n
LOCATION:https://researchseminars.org/talk/TQFT/26/
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