E-polynomials of the SL(2,C)-character varieties of surface groups

Abstract

We compute the E-polynomials of the moduli spaces of representations of the fundamental group of a once-punctured surface of any genus into SL(2,C), for any possible holonomy around the puncture. We follow the geometric technique introduced in arXiv:1106.6011, based on stratifying the space of representations, and on the analysis of the behaviour of the E-polynomial under fibrations.

22 pages, no figures. v2. References added. v3. Typo in matrix of page 17 corrected. arXiv admin note: text overlap with arXiv:1405.7120

References in corpus (3)

• Moduli Spaces of Parabolic Higgs Bundles and Parabolic K(D) Pairs over Smooth Curves: I
• On the E-polynomials of a family of Character Varieties
• E-polynomial of SL(2,C)-character varieties of complex curves of genus 3

Cited by in corpus (3)

• Arithmetic of singular character varieties and their $E$-polynomials
• Virtual classes of parabolic ${\mathrm{SL}}_2(\mathbb{C})$-character varieties
• Serre polynomials of $S{L}_n$- and $PG{L}_n$-character varieties of free groups