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SUMMARY:Scissors automorphism groups and their homology - Robin Sroka (Mü
 nster)
DTSTART:20241127T160000Z
DTEND:20241127T170000Z
UID:TALK220870@talks.cam.ac.uk
CONTACT:Oscar Randal-Williams
DESCRIPTION:Two polytopes in Euclidean n-space are called scissors congrue
 nt if one can be cut into finitely many polytopic pieces that can be rearr
 anged by Euclidean isometries to form the other. A generalized version of 
 Hilbert's third problem asks for a classification of Euclidean n-polytopes
  up to scissors congruence. In this talk\, we consider the complementary q
 uestion and study the scissors automorphism group -- it encodes all transf
 ormations realizing the scissors congruence relation between distinct poly
 topes. This leads to a group-theoretic interpretation of Zakharevich's hig
 her scissors congruence K-theory. By varying the notion of polytope\, scis
 sors automorphism groups recover many important examples of groups appeari
 ng in dynamics and geometric group theory including Brin--Thompson groups 
 and groups of rectangular exchange transformations. Combined with recently
  developed computational tools for scissors congruence K-theory\, we recov
 er and extend calculations of their homology. This talk is based on joint 
 work with Kupers--Lemann--Malkiewich--Miller.
LOCATION:MR13
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