Abstract
For fixed g and T we show the finiteness of the set of affine equivalence classes of flat surfaces of genus g whose Veech group contains a cusp of hyperbolic co-area less than T. We obtain new restrictions on Veech groups: any non-elementary Fuchsian group can appear only finitely many times in a fixed stratum; any non-elementary Veech group is of finite index in its normalizer; and the quotient of ℍ by a non-lattice Veech group admits arbitrarily large embedded disks. A key ingredient of the proof is the finiteness of the set of affine equivalence classes of flat surfaces of genus g whose Veech group contains a hyperbolic element with eigenvalue less than T.
Original language | English |
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Pages (from-to) | 313-336 |
Number of pages | 24 |
Journal | Commentarii Mathematici Helvetici |
Volume | 85 |
Issue number | 2 |
DOIs | |
State | Published - 9 Mar 2010 |
Keywords
- Flat surface
- Fuchsian group
- Markov partition
- Veech group
ASJC Scopus subject areas
- Mathematics (all)