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SUMMARY:Higher Scissors Congruence of Manifolds - Mona Merling (University
  of Pennsylvania)
DTSTART:20230613T133000Z
DTEND:20230613T143000Z
UID:TALK200698@talks.cam.ac.uk
DESCRIPTION:The classical scissors congruence problem asks whether given t
 wo polyhedra with the same volume\, one can cut one into a finite number o
 f smaller polyhedra and reassemble these to form the other. There is an an
 alogous definition of an SK (German "schneiden und kleben\," cut and paste
 ) relation for manifolds and classically defined scissors congruence (SK) 
 groups for manifolds. We can actually lift this to a scissors congruence s
 pectrum which admits a map to the K-theory of Z\, which on pi_0 recovers t
 he Euler characteristic map. I will discuss what this higher homotopical l
 ift of the Euler characteristic sees on the level of pi_1\, and some specu
 lative connections with the cobordism category. This is joint work in part
  with Hoekzema\, Murray\, Rovi and Semikina\, and in part with Raptis and 
 Semikina.
LOCATION:Seminar Room 1\, Newton Institute
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