Quotient groups of the fundamental groups of certain strata of the moduli space of quadratic differentials
Geometry & topology, Tome 14 (2010) no. 2, pp. 1129-1164.

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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.

DOI : 10.2140/gt.2010.14.1129
Keywords: quadratic differential, Teichmüller space, fundamental group

Walker, Katharine C 1

1 Center for Communications Research, 4320 Westerra Court, San Diego, CA 92121
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Walker, Katharine C. Quotient groups of the fundamental groups of certain strata of the moduli space of quadratic differentials. Geometry & topology, Tome 14 (2010) no. 2, pp. 1129-1164. doi : 10.2140/gt.2010.14.1129. http://geodesic.mathdoc.fr/articles/10.2140/gt.2010.14.1129/

[1] J S Birman, Braids, links, and mapping class groups, Annals of Math. Studies 82, Princeton Univ. Press (1974)

[2] D J Copeland, Monodromy of the Hitchin map over hyperelliptic curves, Int. Math. Res. Not. (2005) 1743

[3] A Eskin, H Masur, A Zorich, Moduli spaces of abelian differentials: the principal boundary, counting problems, and the Siegel–Veech constants, Publ. Math. Inst. Hautes Études Sci. (2003) 61

[4] E Fadell, L Neuwirth, Configuration spaces, Math. Scand. 10 (1962) 111

[5] P Griffiths, J Harris, Principles of algebraic geometry, Wiley Classics Library, Wiley (1994)

[6] M Kontsevich, A Zorich, Connected components of the moduli spaces of Abelian differentials with prescribed singularities, Invent. Math. 153 (2003) 631

[7] H V Kronk, R D Ringeisen, A T White, On $2$–cell imbeddings of complete $n$-partite graphs, Colloq. Math. 36 (1976) 295

[8] E Lanneau, Hyperelliptic components of the moduli spaces of quadratic differentials with prescribed singularities, Comment. Math. Helv. 79 (2004) 471

[9] H Masur, J Smillie, Hausdorff dimension of sets of nonergodic measured foliations, Ann. of Math. $(2)$ 134 (1991) 455

[10] H Masur, A Zorich, Multiple saddle connections on flat surfaces and the principal boundary of the moduli spaces of quadratic differentials, Geom. Funct. Anal. 18 (2008) 919

[11] G P Scott, Braid groups and the group of homeomorphisms of a surface, Proc. Cambridge Philos. Soc. 68 (1970) 605

[12] W A Veech, The Teichmüller geodesic flow, Ann. of Math. $(2)$ 124 (1986) 441

[13] K C Walker, Connected components of the strata of quadratic differentials over the Teichmüller space, Geom. Dedicata 142 (2009) 47

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