The space of ending laminations is connected

Geometry & Topology
Event time: 
Thursday, March 1, 2007 - 11:30am to Wednesday, February 28, 2007 - 7:00pm
431 DL
Saul Schleimer
Speaker affiliation: 
Event description: 

The space of ending laminations EL(S) on a surface, S, is
obtained from Thurston’s projectivized space of measured laminations by
removing all non-filling laminations and forgetting the measures. This
arises in several ways; for example, it is a theorem of Klarreich that
EL(S) is the Gromov boundary of the curve complex. We prove that EL(S) is
connected if the genus of S is at least two and S has at least one
puncture. Taking branched covers then yields the result for closed
surfaces with genus at least four. This is joint work with Chris