A collar lemma for Hitchin representations
Dynamics on Moduli Spaces April 13, 2015  April 17, 2015
Location: SLMath: Eisenbud Auditorium
Riemann surfaces
mapping class groups
hyperbolic geometry
hyperbolic manifold
discrete group actions
geodesic inequalities
14215
There is a wellknown 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 nonzero 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 GyeSeon Lee.
Zhang.Notes

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