Contribution Invited speaker
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, I will begin by reviewing coHH of dg coalgebras, with an extension to dg cocategories, and will then present new results in the dg case. To conclude, I will present recent computational results fo coTHH, due to Bohmann, Gerhardt, Høgenhaven, Shipley, and Ziegenhagen.