On Structural Properties of THH and TR

Abstract

This thesis is divided into two parts. In the first part, we prove that topological Hochschild homology satisfies both 1-connected and flat descent for connective E₂₋ rings. Along the way, we provide an alternative construction of the ``May filtration'' on topological Hochschild homology, which was originally considered by Angelini--Knoll and Salch. In the second part of this thesis, which is based on joint work with Jonas McCandless, we show that topological restriction homology has a chromatic vanishing property similar to that of algebraic K-theory and topological cyclic homology. This is based on a careful analysis of the interaction of algebraic K-theory with infinite products.