On the topology of ending lamination space

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.