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L-spaces, taut foliations, and graph manifolds

Part of: Low-dimensional topology

Published online by Cambridge University Press:  23 January 2020

Jonathan Hanselman ,
Jacob Rasmussen ,
Sarah Dean Rasmussen  and
Liam Watson
Jonathan Hanselman
Affiliation:
Department of Mathematics, Princeton University, Fine Hall, Washington Road,Princeton, NJ08540, USA email jh66@math.princeton.edu
Jacob Rasmussen
Affiliation:
Department of Pure Mathematics and Mathematical Statistics,Centre for Mathematical Sciences, Wilberforce Road, CambridgeCB3 0WB, UK email J.Rasmussen@dpmms.cam.ac.uk
Sarah Dean Rasmussen
Affiliation:
Department of Pure Mathematics and Mathematical Statistics,Centre for Mathematical Sciences, Wilberforce Road, CambridgeCB3 0WB, UK email S.Rasmussen@dpmms.cam.ac.uk
Liam Watson
Affiliation:
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, CanadaV6T 1Z2 email liam@math.ubc.ca
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Abstract

If $Y$ is a closed orientable graph manifold, we show that $Y$ admits a coorientable taut foliation if and only if $Y$ is not an L-space. Combined with previous work of Boyer and Clay, this implies that $Y$ is an L-space if and only if $\unicode[STIX]{x1D70B}_{1}(Y)$ is not left-orderable.

Keywords

graph manifoldL-spacetaut foliationHeegaard Floer

MSC classification

Primary: 57M27: Invariants of knots and 3-manifolds
Type
Research Article
Information
Compositio Mathematica , Volume 156 , Issue 3 , March 2020 , pp. 604 - 612
Copyright
© The Authors 2020

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Footnotes

The first author was partially supported by NSF RTG grant DMS-1148490. The second author was partially supported by EPSRC grant EP/M000648/1. The third author was supported by EPSRC grant EP/M000648/1. The fourth author was partially supported by a Marie Curie Career Integration Grant (HFFUNDGRP).

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