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 Nobeling space. Finally if n not equal 0 , then FPML(S) is connected