Small dilatation pseudo-Anosovs and 3-manifolds

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dc.creatorFarb, Benson
dc.creatorLeininger, Christopher J.
dc.creatorMargalit, Dan
dc.date2009-05-02
dc.date.accessioned2026-07-07T13:11:17Z
dc.date.available2026-07-07T13:11:17Z
dc.descriptionThe main result of this paper is a universal finiteness theorem for the set of all small dilatation pseudo-Anosov homeomorphisms, ranging over all surfaces. More precisely, we consider pseudo-Anosovs F:S to S with |chi(S)| log(lambda(F)) bounded above by some constant, and we prove that, after puncturing the surfaces at the singular points of the stable foliations, the resulting set of mapping tori is finite. Said differently, there is a finite set of fibered hyperbolic 3-manifolds so that all small dilatation pseudo-Anosovs occur as the monodromy of a Dehn filling on one of the 3-manifolds in the finite list, where the filling is on the boundary slope of a fiber.
dc.description40 pages, 6 color figures
dc.identifierhttps://arxiv.org/abs/0905.0219
dc.identifierhttp://arxiv.org/abs/0905.0219
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/229240
dc.subjectGeometric Topology
dc.subjectDynamical Systems
dc.subject57M50 (primary); 15A18, 30F60, 37E30 (secondary)
dc.titleSmall dilatation pseudo-Anosovs and 3-manifolds
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