Kathryn Hess: Topological coHochschild homology

(Joint work with Brooke Shipley)

Topological Hochschild homology (THH) is a version for ring spectra of classical Hochschild homology of rings, the importance of which is due primarily to its close connection to algebraic K-theory, mediated by the Dennis trace map.  In this talk, I will introduce a dual version of THH for coalgebra spectra, called topological co-Hochschild homology (coTHH), which is a spectral version of coHochschild homology (coHH) of dg coalgebras, and explain its relationship to both THH and algebraic K-theory, also expressed in terms of a trace map.

As a warm up in the first hour, I will begin by reviewing (co)HH of dg (co)algebras, with an extension to dg cocategories.  In the second hour I will present new results in the dg case, as well as recent computational results for coTHH, due to Bohmann, Gerhardt, Høgenhaven, Shipley, and Ziegenhagen.