Abstract
We say that a collection of geodesics in the hyperbolic plane is a modular pattern if is invariant under the modular group , if there are only finitely many –equivalence classes of geodesics in , and if each geodesic in is stabilized by an infinite order subgroup of . For instance, any finite union of closed geodesics on the modular orbifold lifts to a modular pattern. Let be the ideal boundary of . Given two points we write if and are the endpoints of a geodesic in . (In particular .) We will see in §3.2 that is an equivalence relation. We let be the quotient space. We call a modular circle quotient. In this paper we will give a sense of what modular circle quotients “look like” by realizing them as limit sets of piecewise-linear group actions.
Citation
Richard Evan Schwartz. "Modular circle quotients and PL limit sets." Geom. Topol. 8 (1) 1 - 34, 2004. https://doi.org/10.2140/gt.2004.8.1
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