Cut and paste invariants of manifolds via algebraic K-theory

Abstract

Recent work of Jonathan Campbell and Inna Zakharevich has focused on building machinery for studying scissors congruence problems via algebraic $K$-theory, and applying these tools to studying the Grothendieck ring of varieties. In this paper we give a new application of their framework: we construct a $K$-space that recovers the classical $\mathrm{SK}$ ("schneiden und kleben," German for "cut and paste") groups for manifolds on $\pi_0$, and we construct a derived version of the Euler characteristic