Maximal Thurston-Bennequin number and reducible Legendrian surgery

Kouichi Yasui

doi:10.1112/s0010437x1600748x

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arXiv · 1508.05615

Maximal Thurston-Bennequin number and reducible Legendrian surgery

Kouichi Yasui

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Abstract

We give a method for constructing a Legendrian representative of a knot in $S^3$ which realizes its maximal Thurston-Bennequin number under a certain condition. The method utilizes Stein handle decompositions of $D^4$, and the resulting Legendrian representative is often very complicated (relative to the complexity of the topological knot type). As an application, we construct infinitely many knots in $S^3$ each of which yields a reducible 3-manifold by a Legendrian surgery in the standard tight contact structure. This disproves a conjecture of Lidman and Sivek.

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Kouichi Yasui. 2015-08-23. Maximal Thurston-Bennequin number and reducible Legendrian surgery. https://doi.org/10.1112/s0010437x1600748x

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