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Connectivity of the space of ending laminations
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Leininger, Christopher J. and Schleimer, Saul (2009) Connectivity of the space of ending laminations. Duke Mathematical Journal, Vol.150 (No.3). pp. 533-575. doi:10.1215/00127094-2009-059 ISSN 0012-7094.
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Official URL: http://dx.doi.org/10.1215/00127094-2009-059
Abstract
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 [28, Theorem 1.3] 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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Surfaces, Algebraic, Hyperbolic spaces, Curves, Algebraic | ||||
Journal or Publication Title: | Duke Mathematical Journal | ||||
Publisher: | Duke University Press | ||||
ISSN: | 0012-7094 | ||||
Official Date: | 2009 | ||||
Dates: |
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Volume: | Vol.150 | ||||
Number: | No.3 | ||||
Page Range: | pp. 533-575 | ||||
DOI: | 10.1215/00127094-2009-059 | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Funder: | National Science Foundation (U.S.) (NSF) | ||||
Grant number: | DMS-0603881 (NSF), DMS-0508971 (NSF) |
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