Algebraic Geometry Seminar

Combinatorial (or “cut-and-paste”) K-theory is a modern approach to the study of classical scissors congruence group, and can be applied to other geometric settings as well, such as the categories of varieties and semi-algebraic sets. We present the K-theory of squares category as a framework that unifies Waldhausen K-theory as well as many instances of combinatorial K-theory in a natural way. As an application, we lift the Euler characteristic for definable sets in an o-minimal structure to a map of K-theory spectra.