Veering triangulations and Cannon-Thurston maps

François Guéritaud

doi:10.1112/jtopol/jtw016

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arXiv · 1506.03387

Veering triangulations and Cannon-Thurston maps

François Guéritaud

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Abstract

Any hyperbolic surface bundle over the circle gives rise to a continuous surjection from the circle to the sphere, by work of Cannon and Thurston. We prove that the order in which this surjection fills out the sphere is dictated by a natural triangulation of the surface bundle (introduced by Agol) when all singularities of the invariant foliations are at punctures of the fiber.

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François Guéritaud. 2015-06-10. Veering triangulations and Cannon-Thurston maps. https://doi.org/10.1112/jtopol%2Fjtw016

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