Geometry & Topology Volume 15, issue 3 (2011)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Procedure

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Other MSP Journals

Parallelogram decompositions and generic surfaces in $\mathcal{H}^{\mathrm{hyp}}(4)$

Duc-Manh Nguyen

Geometry & Topology 15 (2011) 1707–1747

DOI: 10.2140/gt.2011.15.1707

Bibliography

1	K Calta, Veech surfaces and complete periodicity in genus two, J. Amer. Math. Soc. 17 (2004) 871 MR2083470
2	K Calta, J Smillie, Algebraically periodic translation surfaces, J. Mod. Dyn. 2 (2008) 209 MR2383267
3	A Douady, J Hubbard, On the density of Strebel differentials, Invent. Math. 30 (1975) 175 MR0396936
4	A Eskin, A Okounkov, Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials, Invent. Math. 145 (2001) 59 MR1839286
5	P Hubert, E Lanneau, M Möller, Completely periodic directions and orbit closures of many pseudo-Anosov Teichm\”ller discs in $Q(1,1,1,1)$, to appear in Math. Ann. arXiv:math.GT/0611655
6	P Hubert, E Lanneau, M Möller, The Arnoux–Yoccoz Teichmüller disc, Geom. Funct. Anal. 18 (2009) 1988 MR2491696
7	P Hubert, E Lanneau, M Möller, $\mathrm{GL}_2^+(\R)$–orbit closures via topological splittings, from: "Surveys in differential geometry, Vol. XIV: Geometry of Riemann surfaces and their moduli spaces" (editors L Ji, S A Wolpert, S T Yau), Surv. Differ. Geom. 14, Int. Press (2009) 145 MR2655326
8	P Hubert, T A Schmidt, An introduction to Veech surfaces, from: "Handbook of dynamical systems. Vol. 1B" (editors B Hasselblatt, A Katok), Elsevier (2006) 501 MR2186246
9	M Kontsevich, A Zorich, Connected components of the moduli spaces of Abelian differentials with prescribed singularities, Invent. Math. 153 (2003) 631 MR2000471
10	H Masur, Interval exchange transformations and measured foliations, Ann. of Math. $(2)$ 115 (1982) 169 MR644018
11	H Masur, S Tabachnikov, Rational billiards and flat structures, from: "Handbook of dynamical systems, Vol. 1A" (editors B Hasselblatt, A Katok), North-Holland (2002) 1015 MR1928530
12	C T McMullen, Dynamics of $\mathrm{SL}_2(\mathbb R)$ over moduli space in genus two, Ann. of Math. $(2)$ 165 (2007) 397 MR2299738
13	W P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. $($N.S.$)$ 19 (1988) 417 MR956596
14	W A Veech, Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards, Invent. Math. 97 (1989) 553 MR1005006
15	W A Veech, Moduli spaces of quadratic differentials, J. Analyse Math. 55 (1990) 117 MR1094714
16	A Zorich, Flat surfaces, from: "Frontiers in number theory, physics, and geometry I" (editors P Cartier, B Julia, P Moussa, P Vanhove), Springer (2006) 437 MR2261104