Birgit Richter: Juggling formulae for higher THH
Channel: Hausdorff Center for Mathematics
Date: 29/06/2017

The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields.

Topological Hochschild homology (THH) is the target of the trace map from algebraic K-theory. Similarly, iterated algebraic K-theory maps to an iterated version of THH, the so-called torus homology. In joint work with Halliwell, Hoening, Lindenstrauss and Zakharevich and further joint work with Lindenstrauss we develop juggling formulae for higher order THH, and more generally, relating X-homology of a commutative ring spectrum to its ΣX-homology for a simplicial set X. We apply these results in concrete examples, gaining for instance a relationship between higher order Hochschild and higher order Shukla homology.