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# A collar lemma for Hitchin representations

## Dynamics on Moduli Spaces April 13, 2015 - April 17, 2015

April 13, 2015 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Tengren Zhang (University of Michigan)
Location: MSRI: Simons Auditorium
Tags/Keywords
• Riemann surfaces

• mapping class groups

• hyperbolic geometry

• hyperbolic manifold

• discrete group actions

• geodesic inequalities

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

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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.

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