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WildSurfaces.LatticePropertyr1.1 - 08 Feb 2006 - 10:59 - ThierryMonteiltopic end

Lattice property

Brief definition

Since $SL(2,\mathbb{R})$ acts on $\mathbb{R}^2$ , it also acts on the space of translation surfaces (in the charts).

For any translation surface S, let us denote V(S) the stabiliser of S under the action of $SL(2,\mathbb{R})$ . V(S) is called the Veech group of S. His size measures the level of symmetry of the surface.

A translation surface S is said to have the lattice property if its Veech group V(S) is a lattice in $SL(2,\mathbb{R})$ . Such surfaces are also called Veech surfaces.

References

http://www.orst.edu/~schmidtt/ourPapers/Hubert/intVchGpsX04.pdf
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