Geodesic
Veech groups of infinite-genus surfaces
Ramírez Maluendeas, Camilo1 ; Valdez, Ferrán2
1Fundación Universitaria Konrad Lorenz, Carrero 9 bis #62-43, Bogotá, Colombia
2Center of Mathematical Sciences, National Autonomous University of Mexico (UNAM), Campus Morelia, C.P. 58190, Morelia, Mexico
Algebraic and Geometric Topology, Tome 17 (2017) no. 1, pp. 529-560
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We show that every countable subgroup G < GL+(2, ℝ) without contracting elements is the Veech group of a tame translation surface S of infinite genus for infinitely many different topological types of S. Moreover, we prove that as long as every end has genus, there are no restrictions on the topological type of S to realize all possible uncountable Veech groups.

DOI : 10.2140/agt.2017.17.529
Classification : 20F65, 53A99
Keywords: infinite type translation surface, Veech group

Ramírez Maluendeas, Camilo  1   ; Valdez, Ferrán  2

1 Fundación Universitaria Konrad Lorenz, Carrero 9 bis #62-43, Bogotá, Colombia
2 Center of Mathematical Sciences, National Autonomous University of Mexico (UNAM), Campus Morelia, C.P. 58190, Morelia, Mexico 
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Ramírez Maluendeas, Camilo; Valdez, Ferrán. Veech groups of infinite-genus surfaces. Algebraic and Geometric Topology, Tome 17 (2017) no. 1, pp. 529-560. doi: 10.2140/agt.2017.17.529

[1] J P Bowman, F Valdez, Wild singularities of flat surfaces, Israel J. Math. 197 (2013) 69 | DOI

[2] J Dugundji, Topology, Allyn and Bacon (1966)

[3] É Ghys, Topologie des feuilles génériques, Ann. of Math. 141 (1995) 387 | DOI

[4] W P Hooper, B Weiss, Generalized staircases: recurrence and symmetry, Ann. Inst. Fourier (Grenoble) 62 (2012) 1581 | DOI

[5] A S Kechris, Classical descriptive set theory, 156, Springer (1995) | DOI

[6] S Mazurkiewicz, W Sierpiński, Contribution à la topologie des ensembles dénombrables, Fundam. Math. 1 (1920) 17

[7] A Phillips, D Sullivan, Geometry of leaves, Topology 20 (1981) 209 | DOI

[8] P Przytycki, G Schmithüsen, F Valdez, Veech groups of Loch Ness monsters, Ann. Inst. Fourier (Grenoble) 61 (2011) 673 | DOI

[9] I Richards, On the classification of noncompact surfaces, Trans. Amer. Math. Soc. 106 (1963) 259 | DOI

[10] E Specker, Die erste Cohomologiegruppe von Überlagerungen und Homotopie-Eigenschaften dreidimensionaler Mannigfaltigkeiten, Comment. Math. Helv. 23 (1949) 303 | DOI

[11] F Valdez, Infinite genus surfaces and irrational polygonal billiards, Geom. Dedicata 143 (2009) 143 | DOI

[12] W A Veech, Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards, Invent. Math. 97 (1989) 553 | DOI

[13] B Von Kerékjártó, Vorlesungen über Topologie I : Flächentopologie, 8, Springer (1923) | DOI

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