TL;DR
This paper investigates the topological properties of the ending lamination space for certain surfaces, establishing its connectivity, local connectivity, and homeomorphism to a Nobeling space in specific cases.
Contribution
It provides new topological characterizations of the ending lamination space, including its connectivity, local connectivity, and a homeomorphism to a Nobeling space for genus zero surfaces.
Findings
EL(S) is (n-1)-connected and (n-1)-locally connected for surfaces with 3g+p > 4.
dim(PML(S))=2n+1=6g+2p-7.
EL(S) is homeomorphic to the p-4 dimensional Nobeling space when g=0.
Abstract
We show that if S is a finite type orientable surface of genus g and p punctures where 3g+p > 4, 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 Nobeling space.
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