Abstract
A contact foliation is a foliation endowed with a leafwise contact structure. In this remark we explain a turbulisation procedure that allows us to prove that tightness is not a homotopy invariant property for contact foliations.
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Acknowledgements
This note was developed during a visit of the author to V. Ginzburg in UCSC and it was V. Ginzburg that posed the question of whether tightness could potentially be stable under deformations. In this occasion the question is certainly more clever than the small observation that provides the (negative) answer. The author is also grateful to F. Presas for reading this note and providing valuable suggestions. The author is supported by the NWO Vici Grant No. 639.033.312 of Marius Crainic.
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del Pino, Á. Some tight contact foliations can be approximated by overtwisted ones. Arch. Math. 110, 413–419 (2018). https://doi.org/10.1007/s00013-017-1139-8
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DOI: https://doi.org/10.1007/s00013-017-1139-8