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Corpus ID: 119297945

Simple loops on punctured surfaces and boundaries of character varieties

@article{Whang2016SimpleLO,
title={Simple loops on punctured surfaces and boundaries of character varieties},
author={Junho Peter Whang},
journal={arXiv: Algebraic Geometry},
year={2016}
}

We prove that every relative moduli space of complex special linear local systems of rank two on a punctured surface is log Calabi-Yau, in that it has a normal projective compactification with anticanonical boundary divisor. We connect this to another result that the generating series for multicurves counted by word length on a punctured surface satisfies a universal symmetry.

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We study the Diophantine geometry of algebraic curves on relative moduli of special linear rank two local systems over surfaces. We prove that the set of integral points on any nondegenerately… Expand

We establish a structure theorem for the integral points on moduli of special linear rank two local systems over surfaces, using mapping class group descent and boundedness results for systoles of… Expand

Moduli spaces of points on $n$-spheres carry natural actions of braid groups. For $n=0$, $1$, and $3$, we prove that these symmetries extend to actions of mapping class groups of positive genus… Expand

We develop a Diophantine analysis on moduli of special linear rank two local systems over surfaces with prescribed boundary traces. We first show that such a moduli space is a log Calabi-Yau variety… Expand