Ellipses in translation surfaces

Details Ellipses in translation surfaces Ellipses in translation surfaces

2010-03-08

arxiv.org/abs/1003.1672v2

Mathematics

Geometric Topology

revised based on referee's comments. 40 pages, 4 figures

Scientific paper

We characterize subgroups of the mapping class group that stabilize a Teichmueller disk in terms of ellipses and strips that are immersed in the associated translation surface. In particular, we show that the space of immersed ellipses/strips that meet at least three cone points is naturally a (non-manifold) 2-dimensional cell complex. The topology of this complex and the geometry of its 0-cells determine the translation surface and its affine diffeomorphism group (up to the kernel of the differential).

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