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Connectivity of the space of ending laminations

By Christopher J. Leininger and Saul Schleimer

Abstract

We prove that for any closed surface of genus at least four, and any punctured surface\ud of genus at least two, the space of ending laminations is connected. A theorem of E.\ud Klarreich [28, Theorem 1.3] implies that this space is homeomorphic to the Gromov\ud boundary of the complex of curves. It follows that the boundary of the complex of curves\ud is connected in these cases, answering the conjecture of P. Storm. Other applications\ud include the rigidity of the complex of curves and connectivity of spaces of degenerate\ud Kleinian groups

Topics: QA
Publisher: Duke University Press
Year: 2009
OAI identifier: oai:wrap.warwick.ac.uk:3138

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