From loom spaces to veering triangulations

Abstract: A ``loom space'' is a copy of $\mathbb{R}^2$ equipped with a pair of transverse foliations satisfying certain axioms. These arise as the link spaces associated to veering triangulations and also as the flow spaces of (drilled) pseudo-Anosov flows without perfect fits. Following work of Guéritaud, we prove a converse: namely, every loom space gives rise, canonically, to a locally veering triangulation. Furthermore, the realisation of this triangulation (minus the vertices) is homeomorphic to $\mathbb{R}^3$. I will sketch the proof, giving many pictures.

This is joint work with Henry Segerman.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( paper )

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Geometry and topology online

Series comments: You can also find up-to-date information on the seminar homepage - warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/geomtop/

The talks start at 13:30. Talks are typically fifty minutes long, with ten minutes for questions.

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