Ideal Triangulations of Pseudo-Anosov Mapping Tori

By Ian Agol. 2010

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We show how to construct an ideal triangulation of a mapping torus of a pseudo-Anosov map punctured along the singular fibers. This gives rise to a new conjugacy invariant of mapping classes, and a new proof of a theorem of Farb-Leininger-Margalit. The approach in this paper is based on ideas of Hamenstadt.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/85125698300bd13a3f411809ad78ec3a7d0a161d