Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 13, Number 6 (2013), 3537-3602.
Minimal dilatations of pseudo-Anosovs generated by the magic $3$–manifold and their asymptotic behavior
This paper concerns the set of pseudo-Anosovs which occur as monodromies of fibrations on manifolds obtained from the magic –manifold by Dehn filling three cusps with a mild restriction. Let be the manifold obtained from by Dehn filling one cusp along the slope . We prove that for each (resp. ), the minimum among dilatations of elements (resp. elements with orientable invariant foliations) of defined on a closed surface of genus is achieved by the monodromy of some –bundle over the circle obtained from or by Dehn filling both cusps. These minimizers are the same ones identified by Hironaka, Aaber and Dunfield, Kin and Takasawa independently. In the case we find a new family of pseudo-Anosovs defined on with orientable invariant foliations obtained from or by Dehn filling both cusps. We prove that if is the minimal dilatation of pseudo-Anosovs with orientable invariant foliations defined on , then
where is the minimal dilatation of pseudo-Anosovs on an –punctured disk. We also study monodromies of fibrations on . We prove that if is the minimal dilatation of pseudo-Anosovs on a genus surface with punctures, then
Algebr. Geom. Topol., Volume 13, Number 6 (2013), 3537-3602.
Received: 18 October 2011
Revised: 15 February 2013
Accepted: 19 February 2013
First available in Project Euclid: 19 December 2017
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Kin, Eiko; Kojima, Sadayoshi; Takasawa, Mitsuhiko. Minimal dilatations of pseudo-Anosovs generated by the magic $3$–manifold and their asymptotic behavior. Algebr. Geom. Topol. 13 (2013), no. 6, 3537--3602. doi:10.2140/agt.2013.13.3537. https://projecteuclid.org/euclid.agt/1513715740