# Sutured Floer homology, fibrations, and taut depth one foliations

Altman, I
Friedl, S
Juhasz, A

## Publication Date:

17 September 2016

## Journal:

Transactions of the American Mathematical Society

## Last Updated:

2019-08-12T14:07:50.127+01:00

9

368

## DOI:

10.1090/tran/6610

6363-6389

## 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,g) detects which classes in H^1(M) admit a taut depth one foliation such that the only compact leaves are the components of  R(g). 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 Spin^c-structure 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) is not 0, assuming the corresponding group SFH(M,g,s) has non-trivial Euler characteristic.

607569

Submitted

Journal Article