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A collar lemma for Hitchin representations

Presenter
April 13, 2015
Keywords:
  • Riemann surfaces
  • mapping class groups
  • hyperbolic geometry
  • hyperbolic manifold
  • discrete group actions
  • geodesic inequalities
MSC:
  • 32G15
  • 32Fxx
  • 53D18
  • 53Dxx
  • 37-xx
  • 30Fxx
  • 30F60
  • 30F35
Abstract
There is a well-known result known as the collar lemma for hyperbolic surfaces. It has the following consequence: if two closed curves, a and b, on a closed orientable hyperbolizable surface have non-zero geometric intersection number, then there is an explicit lower bound for the length of a in terms of the length of b, which holds for any hyperbolic structure one can choose on the surface. Furthermore, this lower bound for the length of a grows logarithmically as we shrink the length of b. By slightly weakening this lower bound, we generalize this statement to hold for all Hitchin representations instead of just hyperbolic structures. This is joint work with Gye-Seon Lee.
Supplementary Materials