Strongly Invertible Legendrian Links

Carlo Collari; Paolo Lisca

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arXiv · 2311.07974

Strongly Invertible Legendrian Links

Carlo Collari·Paolo Lisca

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Abstract

We introduce and study strongly invertible Legendrian links in the standard contact three-dimensional space. We establish the equivariant analogs of basic results separately well-known for strongly invertible and Legendrian links, i.e. the existence of transvergent front diagrams, an equivariant Legendrian Reidemeister theorem, and an equivariant stabilization theorem \`a la Fuch-Tabachnikov. We also introduce a maximal equivariant Thurston-Bennequin number for strongly invertible links and we exhibit infinitely many such links for which the invariant coincides with the usual maximal Thurston-Bennequin number. We conjecture that such a coincidence does not hold general and that there exist strongly invertible knots having Legendrian representatives isotopic to their reversed Legendrian mirrors but not isotopic to any strongly invertible Legendrian knot.

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Carlo Collari, Paolo Lisca. 2023-11-14. Strongly Invertible Legendrian Links. https://arxiv.org/abs/2311.07974

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