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arXiv · 1910.14357

Orbit Growth Of Contact Structures After Surgery

Patrick Foulon·Boris Hasselblatt·Anne Vaugon
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Abstract

Investigation of the effects of a contact surgery construction and of invariance of contact homology reveals a rich new field of inquiry at the intersection of dynamical systems and contact geometry. We produce contact 3-flows not topologically orbit-equivalent to any algebraic flow, including examples on many hyperbolic 3-manifolds, and we show how the surgery produces dynamical complexity for any Reeb flow compatible with the resulting contact structure. This includes exponential complexity when neither the surg-ered flow nor the surgered manifold are hyperbolic. We also demonstrate the use in dynamics of contact homology, a powerful tool in contact geometry.

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Patrick Foulon, Boris Hasselblatt, Anne Vaugon. 2019-10-31. Orbit Growth Of Contact Structures After Surgery. https://arxiv.org/abs/1910.14357

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