Veech groups without parabolic elements

By Pascal Hubert, Erwan Lanneau. 2005

56 citations recorded by the source corpus.

We prove that a ``bouillabaisse'' surface (translation surface which has two transverse parabolic elements) has totally real trace field. As a corollary, non trivial Veech groups which have no parabolic elements do exist. The proof follows Veech's viewpoint on Thurston's construction of pseudo-Anosov diffeomorphisms.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c7d8b3e7b92b3e4db92ccd73fe27b2e0c24f39b9

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In Computational Theory and Mathematics

1. G. Forni
2. Martin Möller
3. Matt Bainbridge

In Geometry and Topology

1. G. Forni
2. Martin Möller
3. Matt Bainbridge
4. Carlos Matheus
5. A. Eskin
6. A. Zorich
7. Alexander I. Bufetov
8. J. Yoccoz

In Mathematical Physics

1. Martin Möller
2. G. Forni
3. Matt Bainbridge
4. Carlos Matheus
5. Alexander I. Bufetov
6. A. Eskin
7. A. Zorich
8. J. Yoccoz

Citations in the corpus

• A geometric criterion for the non-uniform hyperbolicity of the Kontsevich--Zorich cocycle (2010, background): “) ⊂ P1(R) of completely periodic directions has at least two 30 GIOVANNI FORNI WITH AN APPENDIX BY CARLOS MATHEUS distinct elements. It is called a prelattice surface (or a bouillabaisse surface, see [HuLa]) if its Veech group SL(ω) contains two transverse parabolic elements. Any prelattice surface ”
• The Deligne–Mumford compactification of the real multiplication locus and Teichmüller curves in genus 3 (2012, background): “The trace field of (X,ω) is a number field which is totally real (see [Möl06b] or [HL06]) whose degree is at most the genus of X (see [McM03]).”