Connected sums and finite energy foliations I: Contact connected sums

2013/11/30 by Joel W. Fish, Richard Siefring · 1 citation
Mathematics · #math.SG #math.DS #msc:32Q65 #msc:53D42 #msc:37J05

paper · pdf · doi:10.4310/jsg.2018.v16.n6.a4

published as Journal of Symplectic Geometry, 16(6):1639-1748, 2018 · 78 pages, 4 figures; edited to incorporate referee suggestions; accepted for publication in Journal of Symplectic Geometry

arxiv created 2016/08/16 · arxiv updated 2019/03/20

Abstract

We consider a 3-manifold M equipped with nondegenerate contact form λ and compatible almost complex structure J. We show that if the data (M, λ, J) admits a stable finite energy foliation, then for a generic choice of distinct points p, q∈ M, the manifold M' formed by taking the connected sum at p and q admits a nondegenerate contact form λ' and compatible almost complex structure J' so that the data (M', λ', 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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