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

2014/07/25 by J. Martı́nez-Martı́nez, Javier Martinez-Martinez, Vicente Muñoz +3 · 1 citation
Computer Science · Mathematics · #14C30 #14D20 #14L24 #32J25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14C30 #msc:14D20 #msc:14L24 #msc:32J25

paper · pdf · doi:10.48550/arxiv.1407.6975

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

openalex publication_date 2014/07/25 · arxiv created 2020/02/09 · arxiv updated 2020/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The Self-Duality Equations on a Riemann Surface
• On the E-polynomials of a family of Character Varieties
• E-polynomial of SL(2,C)-character varieties of complex curves of genus 3
• Hodge-Deligne polynomials of SL(2,C)-character varieties for curves of small genus

Cited by

• e-polynomials of character varieties

Related

• E-polynomials of PGL(2,ℂ)-character varieties of surface groups
• E-polynomial of SL(2,C)-character varieties of complex curves of genus 3
• Hodge-Deligne polynomials of SL(2,C)-character varieties for curves of small genus
• On the E-polynomial of parabolic Sp_2n-character varieties
• E-Polynomials of Generic GL_n\rtimes < σ > ~-Character Varieties: Unbranched Case