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SUMMARY:The discrete bordism category in dimension 1 - Jan Steinebrunner (
 Oxford)
DTSTART:20191018T150000Z
DTEND:20191018T160000Z
UID:TALK131383@talks.cam.ac.uk
CONTACT:Nils Prigge
DESCRIPTION:The discrete bordism category hCob_d has as objects closed (d-
 1)-manifolds and as morphisms diffeomorphism classes of d-dimensional bord
 isms. This is a simplified version of the topologically enriched bordism c
 ategory Cob_d whose classifying space B(Cob_d) been completely determined 
 by Galatius-Madsen-Tillmann-Weiss in 2006. In comparison\, little is known
  about the classifying space B(hCob_d).\n   \nI will identify B(hCob_1) as
  a circle bundle over a delooping of BCob_2\, showing\, in particular\, th
 at the rational cohomology ring of hCob_1 is polynomial on classes \\kappa
 _i in degrees 2i+2 for all i>=1. The seemingly simpler category hCob_1 hen
 ce has a more complicated classifying space than Cob_1. Moreover\, I will 
 give combinatorial formulas for cocycles on hCob_1 that represent \\kappa_
 i.
LOCATION:MR13
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