Topological cyclic homology of the integers at two Original Research Article

The topological Hochschild homology of the integers image is an S1-equivariant spectrum. We prove by computation that for the restricted C2-action on image the fixed points and homotopy fixed points are equivalent, after passing to connective covers and completing at two. By Tsalidis (1994) a similar statement then holds for the action of every cyclic subgroup C2n subset of S1 of order a power of two. Next we inductively determine the mod two homotopy groups of all the fixed point spectra image, following Bökstedt and Madsen (1994, 1995) and Tsalidis (1994). We also compute the restriction maps relating these spectra, and use this to find the mod two homotopy groups of the topological cyclic homology of the integers TC(Z), and of the algebraic K-theory of the two-adic integers image.