Characterizations of lattice surfaces

Details Characterizations of lattice surfaces Characterizations of lattice surfaces

2008-09-22

arxiv.org/abs/0809.3729v1

Mathematics

Dynamical Systems

Scientific paper

We answer a question of Vorobets by showing that the lattice property for flat surfaces is equivalent to the existence of a positive lower bound for the areas of affine triangles. We show that the set of affine equivalence classes of lattice surfaces with a fixed positive lower bound for the areas of triangles is finite and we obtain explicit bounds on its cardinality. We deduce several other characterizations of the lattice property.

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