TY - JOUR
T1 - Connectivity of the space of ending laminations
AU - Leininger, Christopher J.
AU - Schleimer, Saul
PY - 2009/12
Y1 - 2009/12
N2 - 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.
AB - 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.
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U2 - 10.1215/00127094-2009-059
DO - 10.1215/00127094-2009-059
M3 - Article
AN - SCOPUS:77957076195
SN - 0012-7094
VL - 150
SP - 533
EP - 575
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 3
ER -