Geometric Tate-Swan cohomology of equivariant spectra

Abstract

We sketch a quick and dirty geometric approach to the Tate-Swan cohomology of equivariant spectra, illustrating it with conjectural applications to Atiyah-Segal $K$-theory of circle actions, and a possible geometric model for the topological cyclic homology of the sphere spectrum.

§2.3 and §3.4 revised; references perhaps straightened out. For Graeme Segal and Sir Michael Atiyah