Connectivity of the space of ending laminations

Details Connectivity of the space of ending laminations Connectivity of the space of ending laminations

2008-01-20

arxiv.org/abs/0801.3058v2

Mathematics

Geometric Topology

v2. 38 pages, 6 figures

Scientific paper

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

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