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arXiv · 1705.04649

E-polynomials of $PGL(2,\mathbb{C})$-character varieties of surface groups

Javier Martinez
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Abstract

In this paper, we compute the E-polynomials of the $PGL(2,\mathbb{C})$-character varieties associated to surfaces of genus $g$ with one puncture, for any holonomy around it, and compare it with its Langlands dual case, $SL(2,\mathbb{C})$. The study is based on the stratification of the space of representations and on the analysis of the behaviour of the E-polynomial under fibrations.

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Javier Martinez. 2017-05-12. E-polynomials of $PGL(2,\mathbb{C})$-character varieties of surface groups. https://arxiv.org/abs/1705.04649

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