Research objectives and content
I propose to compute topological Hochschild homology and topological cyclic homology for the ring Z/nZ of integers modulo a number n. By a theorem of Hesselholt and Madsen based on results of R. McCarthy, for Z/nZ, K-theory and topological cyclic homology essentially agree. Training content (objective, benefit and expected impact)
I expect that I will benefit from the very active group in algebraic topology centered around prof. F. Waldhausen in Bielefeld. In particular I believe that the Gamma-rings of M. Lydakis and S. Schwede will be helpful for me. Gamma-rings are a particular kind of rings up to homotopy, that go well well into the construction of topological Hochschild and Waldhausen's so-called A-theory. I also think that I will have good chances to get a deeper understanding of Waldhausen's A-theory in Bielefeld.
Links with industrial relevance (22)