Essential open book foliation and fractional Dehn twist coefficient

Abstract

We introduce an essential open book foliation, a refinement of the open book foliation, 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' of overtwisted contact structures and a 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.

58 pages, 35 figures

References in corpus (1)

• Reeb vector fields and open book decompositions

Cited by in corpus (8)

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• Quasi right-veering braids and non-loose links
• Visualizing overtwisted discs in open books
• Tight Planar Contact Manifolds with Vanishing Heegaard Floer Contact Invariants
• On the question of genericity of hyperbolic knots
• Overtwisted discs in planar open books
• On a relation between the self-linking number and the braid index of closed braids in open books