Examples of character varieties in characteristic p and ramification

2019/05/17 by Luisa Paoluzzi, Joan Porti, Paoluzzi, Luisa +1 · 1 citation
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.1905.07196

Abstract

We study SL₂(\mathbbF)-character varieties of knots over algebraically closed fields \mathbbF. We give a sufficient condition in terms of the double branched cover of a 2-bridge knot (or, equivalently, of its Alexander polynomial) on the characteristic of \mathbbF, an odd prime, for the SL₂(\mathbbF)-character variety to present ramification phenomena. Finally we provide several explicit computations of character varieties to illustrate the result, exhibiting also other types of ramification.

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• The \rm SL(2,ℂ)-character variety of 8₁₈

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