A collar lemma for Hitchin representations
Dynamics on Moduli Spaces April 13, 2015 - April 17, 2015
Location: MSRI: Simons Auditorium
mapping class groups
discrete group actions
32G15 - Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]
53Dxx - Symplectic geometry, contact geometry [See also 37Jxx, 70Gxx, 70Hxx]
37-XX - Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
30F35 - Fuchsian groups and automorphic functions [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx]
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.
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