On the cohomology of character stacks for non-orientable surfaces

Abstract

We give a counterexample to a formula suggested by the work of Letellier and Rodriguez-Villegas (arXiv:2008.13435) for the mixed Poincaré series of character stacks for non-orientable surfaces. The counterexample is obtained by an explicit description of these character stacks for (real) elliptic curves.

arXiv comment15 pages. All comments are welcome! V2: Minor changes in the exposition and the title, corrected some typos