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arXiv · 1311.4221

Connected sums and finite energy foliations I: Contact connected sums

Joel W. Fish·Richard Siefring
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Abstract

We consider a $3$-manifold $M$ equipped with nondegenerate contact form $\lambda$ and compatible almost complex structure $J$. We show that if the data $(M, \lambda, J)$ admits a stable finite energy foliation, then for a generic choice of distinct points $p$, $q\in M$, the manifold $M'$ formed by taking the connected sum at $p$ and $q$ admits a nondegenerate contact form $\lambda'$ and compatible almost complex structure $J'$ so that the data $(M', \lambda', J')$ also admits a stable finite energy foliation. Along the way, we develop some general theory for the study of finite energy foliations.

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Joel W. Fish, Richard Siefring. 2013-11-17. Connected sums and finite energy foliations I: Contact connected sums. https://doi.org/10.4310/jsg.2018.v16.n6.a4

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