A new approach to topological cyclic homology

Hochschild homology as well as its topological analogue THH are by now well understood from a conceptual point of view (for example as a special case of factorisation homology which is a topological field theory). Then as a secondary invariant from that Connes defined cyclic homology and negative cyclic homology. The topological analogue of cyclic homology as defined by Bökstedt, Hsiang, Madsen however is more involved and relies on point set models. We will give a new and more conceptual description of that. This is report on joint work with P. Scholze.