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Measured laminations and train tracks on infinite surfaces

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Dragomir Saric (CUNY)

Abstract: We introduce a class of train tracks on infinite hyperbolic surfaces in order to parametrize the space of measured laminations by the edge weight systems. We prove that the weak* topology on the measured laminations corresponds to the poinwise convergence topology on the edge weight systems.
When one considers the Teichmuller space of infinite surfaces, a natural subspace of bounded measured laminations produces Thurston boundary and earthquake deformations in the Teichmuller space. We characterize edge weight systems that give rise to bounded measured laminations for surfaces of bounded geometry. Further, we show that the correspondence between the bounded measured laminations and their edge weight systems is a homeomorphism for the uniform weak* topology and the supremum norm topology, correspondingly.