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modular circle quotients and PL limit sets
by
Richard Schwartz
University of Maryland, College Park
I will discuss a theoretical analogue of the question "What does your tennis racket look like if it is strung so tightly that the individual strings collapse into points". More precisely, I will consider topological quotients of the circle based on patterns of geodesics in the hyperbolic plane which have modular-group symmetry. Given one of these patterns, one identifies two points of the circle if they are the endpoints of a geodesics in the pattern. I will show how to realize the resulting quotient spaces as limit sets of groups acting on the sphere - of possibly high dimension - by piecewise linear homeomorphisms.
Date received: May 2, 2003
Copyright © 2003 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # calc-18.