Orbifold K\"ahler Groups related to Mapping Class groups

TL;DR

This paper constructs orbifold compactifications of moduli stacks of pointed stable curves and uses quantum representations to analyze their fundamental groups, providing new K"ahler groups and addressing the Shafarevich conjecture.

Contribution

It introduces orbifold compactifications of moduli stacks and employs TQFT representations to study their fundamental groups, advancing understanding of K"ahler groups and the Shafarevich conjecture.

Findings

Constructed orbifold compactifications of moduli stacks

Used quantum representations to analyze fundamental groups

Provided counterexamples related to the Shafarevich conjecture

Abstract

We construct certain orbifold compactifications of the moduli stack of pointed stable curves over $\mathbb C$ and study their fundamental groups by means of their quantum representations. This enables to construct interesting K\"ahler groups and to settle most of the candidates for a counter-example to the Shafarevich conjecture on holomorphic convexity proposed in 1998 by Bogomolov and Katzarkov, using TQFT representations of the mapping class groups.