### Symmetric ring spectra and topological Hochschild homology, by Brooke Shipley

Symmetric spectra were introduced by Jeff Smith as a symmetric monoidal
category of spectra. In this paper, a detection functor is defined which
detects stable equivalences of symmetric spectra. This detection functor is
useful because the classic stable homotopy groups do not detect stable
equivalences in symmetric spectra.

One of the advantages of a symmetric monoidal category of spectra is that one
can define topological Hochschild homology on ring spectra simply by
mimicking the Hochschild complex from algebra. Using the detection functor
mentioned above, this definition of topological Hochschild homology is shown
to agree with Bokstedt's original definition. In particular, this shows that
Bokstedt's definition is correct even for non-connective non-convergent
symmetric ring spectra.

Brooke Shipley <bshipley@math.uchicago.edu>