Sutured Floer homology, fibrations, and taut depth one foliations
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- by Irida Altman, Stefan Friedl and András Juhász PDF
- Trans. Amer. Math. Soc. 368 (2016), 6363-6389 Request permission
Abstract:
For an oriented irreducible 3-manifold $M$ with non-empty toroidal boundary, we describe how sutured Floer homology ($SFH$) can be used to determine all fibred classes in $H^1(M)$. Furthermore, we show that the $SFH$ of a balanced sutured manifold $(M,\gamma )$ detects which classes in $H^1(M)$ admit a taut depth one foliation such that the only compact leaves are the components of $R(\gamma )$. The latter had been proved earlier by the first author under the extra assumption that $H_2(M)=0$. The main technical result is that we can obtain an extremal $\operatorname {Spin}^c$-structure $\mathfrak {s}$ (i.e., one that is in a ‘corner’ of the support of $SFH$) via a nice and taut sutured manifold decomposition even when $H_2(M) \neq 0$, assuming the corresponding group $SFH(M,\gamma ,\mathfrak {s})$ has non-trivial Euler characteristic.References
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Additional Information
- Irida Altman
- Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
- Email: irida.altman@gmail.com
- Stefan Friedl
- Affiliation: Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany
- MR Author ID: 746949
- Email: sfriedl@gmail.com
- András Juhász
- Affiliation: Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom
- Email: juhasza@maths.ox.ac.uk
- Received by editor(s): December 9, 2013
- Received by editor(s) in revised form: August 18, 2014
- Published electronically: November 17, 2015
- Additional Notes: The third author was supported by a Royal Society Research Fellowship and OTKA grant NK81203
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 6363-6389
- MSC (2010): Primary 57M25, 57M27, 57R30
- DOI: https://doi.org/10.1090/tran/6610
- MathSciNet review: 3461037