Ergodic Theory and Dynamical Systems

Research Article

Measured foliations and handlebodies

Howard Masura1

a1 Department of Mathematics, University of Illinois, Chicago, IL 60680, USA

Abstract

We consider the action of the subgroup of the mapping class group consisting of homeomorphisms that extend to the handlebody on Thurston's sphere of measured foliations. Properties of the limit set and domain of discontinuity are described and for genus two it is shown the limit set has measure zero.

(Received February 20 1984)

(Revised March 05 1985)

(Revised June 07 1985)