Kathryn Hess: Topological coHochschild homology
Tid: On 2017-02-01 kl 13.15 - 15.00
Plats: Room 3418, KTH
Medverkande: Kathryn Hess, École Polytechnique Fédérale de Lausanne
(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.