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Essential open book foliations and fractional Dehn twist coefficient
Journal article   Peer reviewed

Essential open book foliations and fractional Dehn twist coefficient

Tetsuya Ito and Keiko Kawamuro
Geometriae Dedicata, Vol.187(1), pp.17-67
04/2017
DOI: 10.1007/s10711-016-0188-7

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Abstract

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.
Geometry Mathematics 57R17 Open book foliation Braid foliation Secondary 53D35 Fractional Dehn twist coefficient Primary 57M50 Overtwisted disc

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