Essential open book foliations and fractional Dehn twist coefficient

By Tetsuya Ito, Keiko Kawamuro. 2012

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We introduce essential open book foliations by refining open book foliations, and develop technical estimates of the fractional Dehn twist coefficient (FDTC) of monodromies and the FDTC for closed braids, which we introduce as well. As applications, we quantitatively study the ‘gap’ between overtwisted contact structures and non-right-veering monodromies. We give sufficient conditions for a 3-manifold to be irreducible and atoroidal. We also show that the geometries of a 3-manifold and the complement of a closed braid are determined by the Nielsen–Thurston types of the monodromies of their open book decompositions.

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

View Paper: https://www.semanticscholar.org/paper/e42ddf95bbd62b1286f56f3dcba3587d25bb0391