Geometry & Topology Volume 25, issue 6 (2021)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Marked points on translation surfaces

Paul Apisa and Alex Wright

Geometry & Topology 25 (2021) 2913–2961

DOI: 10.2140/gt.2021.25.2913

Bibliography

1	P Apisa, GL₂ℝ–invariant measures in marked strata : generic marked points, Earle–Kra for strata and illumination, Geom. Topol. 24 (2020) 373 MR4080485
2	P Apisa, A Wright, Generalizations of the Eierlegende-Wollmilchsau, preprint (2020) arXiv:2011.09452
3	A Avila, A Eskin, M Möller, Symplectic and isometric SL(2, ℝ)–invariant subbundles of the Hodge bundle, J. Reine Angew. Math. 732 (2017) 1 MR3717086
4	D Chen, M Möller, Quadratic differentials in low genus: exceptional and non-varying strata, Ann. Sci. Éc. Norm. Supér. 47 (2014) 309 MR3215925
5	R F Coleman, Torsion points on abelian étale coverings of P¹ −{0,1,∞}, Trans. Amer. Math. Soc. 311 (1989) 185 MR974774
6	R F Coleman, A Tamagawa, P Tzermias, The cuspidal torsion packet on the Fermat curve, J. Reine Angew. Math. 496 (1998) 73 MR1605810
7	A Eskin, S Filip, A Wright, The algebraic hull of the Kontsevich–Zorich cocycle, Ann. of Math. 188 (2018) 281 MR3815463
8	A Eskin, C T McMullen, R E Mukamel, A Wright, Billiards, quadrilaterals and moduli spaces, J. Amer. Math. Soc. 33 (2020) 1039 MR4155219
9	A Eskin, M Mirzakhani, Invariant and stationary measures for the SL(2, ℝ) action on moduli space, Publ. Math. Inst. Hautes Études Sci. 127 (2018) 95 MR3814652
10	A Eskin, M Mirzakhani, A Mohammadi, Isolation, equidistribution, and orbit closures for the SL(2, ℝ) action on moduli space, Ann. of Math. 182 (2015) 673 MR3418528
11	S Filip, Semisimplicity and rigidity of the Kontsevich–Zorich cocycle, Invent. Math. 205 (2016) 617 MR3539923
12	S Filip, Splitting mixed Hodge structures over affine invariant manifolds, Ann. of Math. 183 (2016) 681 MR3450485
13	D Grant, D Shaulis, The cuspidal torsion packet on hyperelliptic Fermat quotients, J. Théor. Nombres Bordeaux 16 (2004) 577 MR2144959
14	E Gutkin, P Hubert, T A Schmidt, Affine diffeomorphisms of translation surfaces : periodic points, Fuchsian groups, and arithmeticity, Ann. Sci. École Norm. Sup. 36 (2003) 847 MR2032528
15	P Hubert, M Schmoll, S Troubetzkoy, Modular fibers and illumination problems, Int. Math. Res. Not. 2008 (2008) MR2428145
16	M Kontsevich, A Zorich, Connected components of the moduli spaces of Abelian differentials with prescribed singularities, Invent. Math. 153 (2003) 631 MR2000471
17	A Kumar, R E Mukamel, Real multiplication through explicit correspondences, LMS J. Comput. Math. 19 (2016) 29 MR3540944
18	E Lanneau, Hyperelliptic components of the moduli spaces of quadratic differentials with prescribed singularities, Comment. Math. Helv. 79 (2004) 471 MR2081723
19	E Lanneau, Connected components of the strata of the moduli spaces of quadratic differentials, Ann. Sci. Éc. Norm. Supér. 41 (2008) 1 MR2423309
20	E Lanneau, D M Nguyen, A Wright, Finiteness of Teichmüller curves in non-arithmetic rank 1 orbit closures, Amer. J. Math. 139 (2017) 1449 MR3730926
21	S Lelièvre, T Monteil, B Weiss, Everything is illuminated, Geom. Topol. 20 (2016) 1737 MR3523067
22	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 MR2439000
23	C T McMullen, Teichmüller curves in genus two : discriminant and spin, Math. Ann. 333 (2005) 87 MR2169830
24	C T McMullen, Teichmüller curves in genus two : torsion divisors and ratios of sines, Invent. Math. 165 (2006) 651 MR2242630
25	C T McMullen, R E Mukamel, A Wright, Cubic curves and totally geodesic subvarieties of moduli space, Ann. of Math. 185 (2017) 957 MR3664815
26	M Mirzakhani, A Wright, The boundary of an affine invariant submanifold, Invent. Math. 209 (2017) 927 MR3681397
27	M Mirzakhani, A Wright, Full-rank affine invariant submanifolds, Duke Math. J. 167 (2018) 1 MR3743698
28	M Möller, Periodic points on Veech surfaces and the Mordell–Weil group over a Teichmüller curve, Invent. Math. 165 (2006) 633 MR2242629
29	M Möller, Affine groups of flat surfaces, from: "Handbook of Teichmüller theory, II" (editor A Papadopoulos), IRMA Lect. Math. Theor. Phys. 13, Eur. Math. Soc. (2009) 369 MR2497782
30	T Monteil, On the finite blocking property, Ann. Inst. Fourier (Grenoble) 55 (2005) 1195 MR2157167
31	T Monteil, Finite blocking property versus pure periodicity, Ergodic Theory Dynam. Systems 29 (2009) 983 MR2505325
32	J Smillie, B Weiss, Minimal sets for flows on moduli space, Israel J. Math. 142 (2004) 249 MR2085718
33	P Tzermias, Almost rational torsion points and the cuspidal torsion packet on Fermat quotient curves, Math. Res. Lett. 14 (2007) 99 MR2289623
34	A Wolecki, Illumination in rational billiards, preprint (2019) arXiv:1905.09358v1
35	A Wright, The field of definition of affine invariant submanifolds of the moduli space of abelian differentials, Geom. Topol. 18 (2014) 1323 MR3254934
36	A Wright, Cylinder deformations in orbit closures of translation surfaces, Geom. Topol. 19 (2015) 413 MR3318755