Homotopy K-theory

Summary

Homotopy K-theory, written $KH$, is a version of algebraic K-theory introduced by Weibel that is homotopy invariant by construction. It is obtained by applying nonconnective K-theory to the rings of polynomial functions on algebraic simplices and taking the realization. For regular Noetherian rings it agrees with ordinary K-theory, and in general it combines the ideas of Karoubi–Villamayor K-theory and of Bass's negative K-groups. Weibel showed that $KH$ satisfies excision, which ordinary K-theory does not.