Abstract
We give su.cient 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 veri.ed 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.
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