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math.DS2022
Arithmeticity of the Kontsevich--Zorich monodromies of certain families of square-tiled surfaces
Etienne Bonnafoux, Manuel Kany, Pascal Kattler +5
The variations of Hodge structures of weight one associated to square-tiled surfaces naturally generate interesting subgroups of integral symplectic matrices called Kontsevich--Zor…
math.DS2009★ 5 cited
Veech groups, irrational billiards and stable abelian differentials
Ferran Valdez
We describe Veech groups of flat surfaces arising from irrational angled polygonal billiards or irreducible stable abelian differentials. For irrational polygonal billiards, we pro…
math.DS2008
Infinite genus surfaces and irrational polygonal billiards
Ferran Valdez
We prove that the natural invariant surface associated with the billiard game on an irrational polygonal table is homeomorphic to the Loch Ness monster, that is, the only orientabl…