Ellipses in translation surfacesGeometriae Dedicata (2012)
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).
- translation surface,
- Teichmuller disc,
- affine diffeomorphism group
Citation InformationSean A Broughton and Chris Judge. "Ellipses in translation surfaces" Geometriae Dedicata Vol. 157 (2012) p. 111 - 151 ISSN: 1572-9168
Available at: http://works.bepress.com/allen_broughton/46/