R-covered branched surfaces

Sandra Shields

Vol. 217 (2004), No. 2, 303–330

DOI: 10.2140/pjm.2004.217.303

Abstract

We give sufficient conditions for an R-covered codimension one foliation F of a closed 3-manifold to be carried by an R-covered branched surface; that is, a branched surface carrying only foliations with the R-covered property. These conditions can be readily verified for many examples. In cases where the branched surface is generated by disks, the R-covered property is stable for F in the sense that all nearby foliations are also R-covered.

Milestones

Received: 3 April 2003

Revised: 8 August 2003

Published: 1 December 2004