Closed surface bundles of least volume
By John William Aaber, Nathan M. Dunfield. 2010
60 citations recorded by the source corpus.
Since the set of volumes of hyperbolic 3-manifolds is well ordered, for each fixed g there is a genus-g surface bundle over the circle of minimal volume. Here, we introduce an explicit family of genus-g bundles which we conjecture are the unique such manifolds of minimal volume. Conditional on a very plausible assumption, we prove that this is indeed the case when g is large. The proof combines a soft geometric limit argument with a detailed Neumann-Zagier asymptotic formula for the volumes of Dehn fillings. Our examples are all Dehn fillings on the sibling of the Whitehead manifold, and we also analyze the dilatations of all closed surface bundles obtained in this way, identifying those with minimal dilatation. This gives new families of pseudo-Anosovs with low dilatation, including a genus 7 example which minimizes dilatation among all those with orientable invariant foliations.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/7802edaa7fa898568f935fa35b9525810f189391
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In Geometry and Topology
- E. Hironaka
- Curtis T. McMullen
- Ian Agol
- Martin Möller
- Stefan Friedl
- A. Wright
- Stefano Vidussi
- Martin Moeller
In Mathematical Physics
- E. Hironaka
- Curtis T. McMullen
- Ian Agol
- Stefan Friedl
- Christopher J. Leininger
- Stefano Vidussi
- Martin Moeller
- Nathan M. Dunfield
Citations in the corpus
- Small dilatation mapping classes coming from the simplest hyperbolic braid (2009, methodology): “References [AD] J. Aaber and N. Dunfield.”
- Ideal Triangulations of Pseudo-Anosov Mapping Tori (2010, background): “One ought to be able to improve this estimate from an improvement of the upper bound on δg in the papers [8, 1].”
- Entropy and the clique polynomial (2015, methodology): “For applications of ΘF to the construction of mapping classes with small entropy, see [1, 15, 23, 26, 27].”