## Translational scissors congruence

Series:
Geometry Topology Seminar
Monday, May 13, 2019 - 2:00pm
1 hour (actually 50 minutes)
Location:
Skiles 006
,
Cornell
Organizer:

One of the classical problems in scissors congruence is
this: given two polytopes in $n$-dimensional Euclidean space, when is
it possible to decompose them into finitely many pieces which are
pairwise congruent via translations?  A complete set of invariants is
provided by the Hadwiger invariants, which measure "how much area is
pointing in each direction."  Proving that these give a complete set
of invariants is relatively straightforward, but determining the
relations between them is much more difficult.  This was done by
Dupont, in a 1982 paper. Unfortunately, this result is difficult to
describe and work with: it uses group homological techniques which
produce a highly opaque formula involving twisted coefficients and
relations in terms of uncountable sums.  In this talk we will discuss
a new perspective on Dupont's proof which, together with more
topological simplicial techniques, simplifies and clarifies the
classical results.  This talk is partially intended to be an