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Ellipses in translation surfaces
Geometriae Dedicata (2012)
  • Sean A Broughton
  • Chris Judge
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).
  • ellipse,
  • translation surface,
  • Teichmuller disc,
  • affine diffeomorphism group
Publication Date
Citation Information
Sean A Broughton and Chris Judge. "Ellipses in translation surfaces" Geometriae Dedicata Vol. 157 (2012) p. 111 - 151 ISSN: 1572-9168
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