Veering triangulations and Cannon–Thurston maps. (27th July 2016)

• Record Type: Journal Article
• Authors: Guéritaud, François
• Is Part Of: Journal of topology. Volume 9:Part 3(2016)
• Page Start: 957
• Page End: 983
• Publication Date: 2016-07-27
• Subjects: Topology -- Periodicals; 514.05
• DOI: 10.1112/jtopol/jtw016
• Languages: English
• ISSNs: 1753-8416

Abstract

Abstract : Any hyperbolic surface bundle over the circle gives rise to a continuous surjection from the circle to the sphere, by work of Cannon–Thurston and Bowditch. 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.