Moscow Mathematical Journal

Volume 25, Issue 1, January–March 2025 pp. 91–149.

Legendrian Lavrentiev Links

Authors: Maxim Prasolov (1)
Author institution:(1) Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkina Str., Moscow 119991, Russia;
Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia

Summary:

Lavrentiev curves form a special class of rectifiable curves, which includes cusp-free piecewise smooth curves. We say that a Lavrentiev curve is Legendrian if the integral of the contact form equals zero on any its subarc. We define Legendrian isotopies of such curves and prove that the equivalence classes of Legendrian Lavrentiev links with respect to Legendrian isotopies coincide with smooth classes.

2020 Math. Subj. Class. 57K33.

Keywords: Legendrian links, smoothing, bi-Lipschitz maps.

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