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Maximal Thurston–Bennequin number and reducible Legendrian surgery

  • Kouichi Yasui (a1)

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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Maximal Thurston–Bennequin number and reducible Legendrian surgery

  • Kouichi Yasui (a1)

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