Slope detection, foliations in graph manifolds, and L-spaces

Steven Boyer; Adam Clay

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arXiv · 1510.02378

Slope detection, foliations in graph manifolds, and L-spaces

Steven Boyer·Adam Clay

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Abstract

A graph manifold rational homology $3$-sphere $W$ with a left-orderable fundamental group admits a co-oriented taut foliation, though it is unknown whether it admits a smooth co-oriented taut foliation. In this paper we extend the gluing theorem of arXiv:1401.7726 to graph manifold rational homology solid tori and use this to show that there are smooth foliations on the pieces of $W$ which come close to matching up on its JSJ tori. This is applied to prove that a graph manifold with left-orderable fundamental group is not an L-space.

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Steven Boyer, Adam Clay. 2015-10-08. Slope detection, foliations in graph manifolds, and L-spaces. https://arxiv.org/abs/1510.02378

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