E-polynomials of character varieties for real curves

Thomas John Baird; Michael Lennox Wong

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arXiv · 2006.01288

E-polynomials of character varieties for real curves

Thomas John Baird·Michael Lennox Wong

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Abstract

We calculate the E-polynomial for a class of the (complex) character varieties $\mathcal{M}_n^{\tau}$ associated to a genus $g$ Riemann surface $\Sigma$ equipped with an orientation reversing involution $\tau$. Our formula expresses the generating function $\sum_{n=1}^{\infty} E(\mathcal{M}_n^{\tau}) T^n$ as the plethystic logarithm of a product of sums indexed by Young diagrams. The proof uses point counting over finite fields, emulating Hausel and Rodriguez-Villegas.

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Thomas John Baird, Michael Lennox Wong. 2020-06-01. E-polynomials of character varieties for real curves. https://arxiv.org/abs/2006.01288

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