A trace for higher scissors congruence groups

Inna Zakharevich, Cornell University

Online Talk 

Consider the following group: take the free abelian group generated by $n$-dimensional Euclidean polytopes, and quotient by the relation that when $\mathrm{meas}(P\cap Q)=0$, $[P\cup Q]=[P]+[Q]$. This is the \emph{scissors congruence group} of $n$-dimensional Euclidean space. It classifies polytopes up to cutting up and rearranging. It is also the first in a sequence of groups which encode invariants of cutting and pasting operations.  In this talk we will discuss the construction of invariants on these gross that can detect some nonzero elements in these higher scissors congruence groups.