2002/10/31 by Sergio R. Fenley, Fenley, Sergio R.
Mathematics · #20E08 #20F65 #57M50 #57M60 (primary) 37R85 #57R30 (secondary) #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:20E08 #msc:20F65 #msc:37R85 #msc:57M50 #msc:57M60 #msc:57R30
paper · pdf · doi:10.48550/arxiv.math/0210482
arxiv created 2002/10/31 · arxiv updated 2009/11/30
We analyse the existence question for essential laminations in 3-manifolds. The purpose is to prove that there are infinitely many closed hyperbolic 3-manifolds which do not admit essential laminations. This answers in the negative a question posed by Gabai and Oertel. The proof is obtained by analysing certain group actions on trees and showing that certain 3-manifold groups only have trivial actions on trees. In general the trees are neither simplicial nor metric. There are corollaries concerning the existence question for Reebless foliations and pseudo-Anosov flows.