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

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.

43 pages, 7 figures. Version 2: Minor typos fixed, Section 3 removed and may now be found in arXiv:0804.0434

References in corpus (3)

• Connected components of the moduli spaces of Abelian differentials with prescribed singularities
• A Special Subgroup of the Surface Braid Group
• Monodromy of the Hitchin Map over Hyperelliptic Curves

Cited by in corpus (4)

• Decorated marked surfaces: spherical twists versus braid twists
• Spectral data for G-Higgs bundles
• Monodromy of the SL_2 Hitchin fibration
• Monodromy of Rank 2 Parabolic Hitchin Systems