Characters of surface groups

Abstract

We initiate the study of characters of surface groups and their corresponding tracial representations. We show that any tracial representation can be approximated arbitrarily well in the Wasserstein topology by factorial tracial representations with spectral gap. In particular, we deduce that the space of traces of a surface group is the Poulsen simplex, thereby resolving positively a question posed by Orovitz, Slutsky, and the third author.