Quotient groups of the fundamental groups of certain strata of the moduli space of quadratic differentials

TL;DR

This paper investigates the fundamental groups of specific strata in the moduli space of quadratic differentials, using Abel-Jacobi maps and local surgeries to construct quotient groups, advancing understanding of their algebraic structure.

Contribution

It introduces a novel method combining Abel-Jacobi maps and local surgeries to construct quotient groups of fundamental groups in certain strata.

Findings

Constructed quotient groups for specific strata

Identified properties of the Abel-Jacobi map relevant to the structure

Demonstrated the effectiveness of local surgeries in this context

Abstract

In this paper, we study fundamental groups of strata of the moduli space of quadratic differentials. We use certain properties of the Abel-Jacobi map, combined with local surgeries on quadratic differentials, to construct quotient groups of the fundamental groups for a particular family of strata.