标题： 强可逆的Legendrian链环 显示英文标题

标题： Strongly Invertible Legendrian Links

摘要： 我们引入并研究了标准接触三维空间中的强可逆Legendrian链环。 我们分别建立了对于强可逆和Legendrian链环广为人知的基本结果的等变类似物，即： 横截前视图的存在性，等变Legendrian Reidemeister定理，以及类似Fuch-Tabachnikov的等变稳定化定理。 我们还为强可逆链环引入了一个最大的等变Thurston-Bennequin数，并展示了无限多个这样的链环，其中该不变量与通常的最大Thurston-Bennequin数相吻合。 我们猜想这种吻合并不普遍成立，并且存在强可逆纽结，其Legendrian表示与它们的反向Legendrian镜像同伦，但不与任何强可逆Legendrian纽结同伦。 显示英文摘要

摘要： 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.