A genuine $G$-spectrum for the cut-and-paste $K$-theory of $G$-manifolds

Abstract

Recent work has applied scissors congruence $K$-theory to study classical cut-and-paste ($SK$) invariants of manifolds. This paper proves the conjecture that the squares $K$-theory of equivariant $SK$-manifolds arises as the fixed points of a genuine $G$-spectrum. Our method utilizes the framework of spectral Mackey functors as models for genuine $G$-spectra, and our main technical result is a general procedure for constructing spectral Mackey functors using squares $K$-theory.

16 pages, comments welcome! Final version, accepted for publication in Bulletin of the London Mathematical Society

References in corpus (2)

• Constructing equivariant spectra via categorical Mackey functors
• Algebraic $K$-theory for squares categories