Journal article
Essential open book foliations and fractional Dehn twist coefficient
Geometriae Dedicata, Vol.187(1), pp.17-67
04/2017
DOI: 10.1007/s10711-016-0188-7
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.
Details
- Title: Subtitle
- Essential open book foliations and fractional Dehn twist coefficient
- Creators
- Tetsuya Ito - Department of Mathematics, Graduate School of Science Osaka University 1-1 Machikaneyama Toyonaka Osaka 560-0043 JapanKeiko Kawamuro - Department of Mathematics The University of Iowa Iowa City IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Geometriae Dedicata, Vol.187(1), pp.17-67
- DOI
- 10.1007/s10711-016-0188-7
- ISSN
- 0046-5755
- eISSN
- 1572-9168
- Publisher
- Springer Netherlands; Dordrecht
- Grant note
- DMS-1206770 / National Science Foundation (http://dx.doi.org/10.13039/100000001) Japan Society for the Promotion of Science (http://dx.doi.org/10.13039/501100001691)
- Language
- English
- Date published
- 04/2017
- Academic Unit
- Mathematics
- Record Identifier
- 9983985867002771
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