On the topology of ending lamination space

David Gabai

doi:10.2140/gt.2014.18.2683

On the topology of ending lamination space

David Gabai

Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We show that if S is a finite-type orientable surface of genus g and with p punctures where 3g+p≥5, then EL(S)is (n-1)-connected and (n-1)-locally connected, where dim (PML(S)) = 2n+1=6g+2p-7. Furthermore, if g =0, then EL(S) is homeomorphic to the (p-4)-dimensional Nöbeling space. Finally if n ≠ 0, then FPML(S) is connected.

Original language	English (US)
Pages (from-to)	2683-2745
Number of pages	63
Journal	Geometry and Topology
Volume	18
Issue number	5
DOIs	https://doi.org/10.2140/gt.2014.18.2683
State	Published - Dec 1 2014

All Science Journal Classification (ASJC) codes

Geometry and Topology

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10.2140/gt.2014.18.2683

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abstract = "We show that if S is a finite-type orientable surface of genus g and with p punctures where 3g+p≥5, then EL(S)is (n-1)-connected and (n-1)-locally connected, where dim (PML(S)) = 2n+1=6g+2p-7. Furthermore, if g =0, then EL(S) is homeomorphic to the (p-4)-dimensional N{\"o}beling space. Finally if n ≠ 0, then FPML(S) is connected.",

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N2 - We show that if S is a finite-type orientable surface of genus g and with p punctures where 3g+p≥5, then EL(S)is (n-1)-connected and (n-1)-locally connected, where dim (PML(S)) = 2n+1=6g+2p-7. Furthermore, if g =0, then EL(S) is homeomorphic to the (p-4)-dimensional Nöbeling space. Finally if n ≠ 0, then FPML(S) is connected.

AB - We show that if S is a finite-type orientable surface of genus g and with p punctures where 3g+p≥5, then EL(S)is (n-1)-connected and (n-1)-locally connected, where dim (PML(S)) = 2n+1=6g+2p-7. Furthermore, if g =0, then EL(S) is homeomorphic to the (p-4)-dimensional Nöbeling space. Finally if n ≠ 0, then FPML(S) is connected.

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On the topology of ending lamination space

Abstract

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