Closed minimal surfaces in cusped hyperbolic three-manifolds |
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Authors: | Zheng Huang Biao Wang |
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Institution: | 1.Department of Mathematics, Graduate School of Science,Osaka University,Osaka,Japan;2.Department of Mathematics,The University of Iowa,Iowa City,USA |
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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. |
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