1997/12/30 by William P. Thurston, Thurston, William P. · 2 citations
Mathematics · #57m50 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.DS #math.GR #math.GT #msc:57m50
paper · pdf · doi:10.48550/arxiv.math/9712268
60 pages, 10 figures
arxiv created 1997/12/30 · arxiv updated 2009/11/30
This paper investigates certain foliations of three-manifolds that are hybrids of fibrations over the circle with foliated circle bundles over surfaces: a 3-manifold slithers around the circle when its universal cover fibers over the circle so that deck transformations are bundle automorphisms. Examples include hyperbolic 3-manifolds of every possible homological type. We show that all such foliations admit transverse pseudo-Anosov flows, and that in the universal cover of the hyperbolic cases, the leaves limit to sphere-filling Peano curves. The skew R-covered Anosov foliations of Sergio Fenley are examples. We hope later to use this structure for geometrization of slithered 3-manifolds.