The contact homology of Legendrian knots with maximal Thurston-Bennequin invariant

Abstract

We show that there exists a Legendrian knot with maximal Thurston-Bennequin invariant whose contact homology is trivial. We also provide another Legendrian knot which has the same knot type and classical invariants but nonvanishing contact homology.

11 pages, 3 figures

References in corpus (3)

• An atlas of Legendrian knots
• On arc index and maximal Thurston-Bennequin number
• Augmentations and Rulings of Legendrian Knots

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• Lagrangian cobordism functor in microlocal sheaf theory I
• Exact Lagrangian tori in symplectic Milnor fibers constructed with fillings