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

2008/02/29 by Katharine C. Walker · 12 citations
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Computer science #Geometry #Group (periodic table) #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Moduli #Moduli space #Physics #Pure mathematics #Quadratic equation #Quotient #Space (punctuation) #math.GT #msc:14D20 #msc:30F30

paper · pdf · doi:10.2140/gt.2010.14.1129

published in Geometry & Topology 14(2), 1129-1164 (Mathematical Sciences Publishers) · 43 pages, 7 figures. Version 2: Minor typos fixed, Section 3 removed and may now be found in arXiv:0804.0434

arxiv created 2008/05/18 · openalex publication_date 2010/05/02 · arxiv updated 2014/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

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• Principles of Algebraic Geometry
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