Ellipses in translation surfaces
Geometric Topology
2010-12-24 v2 Differential Geometry
Abstract
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).
Cite
@article{arxiv.1003.1672,
title = {Ellipses in translation surfaces},
author = {S. Allen Broughton and Chris Judge},
journal= {arXiv preprint arXiv:1003.1672},
year = {2010}
}
Comments
revised based on referee's comments. 40 pages, 4 figures