On the topology of ending lamination space

Gabai, David¹

¹ Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544, USA

Geometry & topology, Tome 18 (2014) no. 5, pp. 2683-2745.

Résumé

We show that if $S$ is a finite-type orientable surface of genus $g$ and with $p$ punctures, where $3g+p\ge 5$, then $\mathcal{ℰ}\mathcal{ℒ}\left(S\right)$ is $\left(n-1\right)$–connected and $\left(n-1\right)$–locally connected, where $dim\left(\mathcal{P}\mathcal{ℳ}\mathcal{ℒ}\left(S\right)\right)=2n+1=6g+2p-7$. Furthermore, if $g=0$, then $\mathcal{ℰ}\mathcal{ℒ}\left(S\right)$ is homeomorphic to the $\left(p-4\right)$–dimensional Nöbeling space. Finally if $n\ne 0$, then $\mathcal{ℱ}\mathcal{P}\mathcal{ℳ}\mathcal{ℒ}\left(S\right)$ is connected.

Détail

DOI : 10.2140/gt.2014.18.2683

Classification : 57M50, 20F65
Keywords: Nöbeling, lamination

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