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L-spaces, taut foliations, and graph manifolds

  • Jonathan Hanselman (a1), Jacob Rasmussen (a2), Sarah Dean Rasmussen (a3) and Liam Watson (a4)

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.

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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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References

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L-spaces, taut foliations, and graph manifolds

  • Jonathan Hanselman (a1), Jacob Rasmussen (a2), Sarah Dean Rasmussen (a3) and Liam Watson (a4)

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