Chekanov-type theorem for spherized cotangent bundles

TL;DR

This paper proves a Chekanov-type theorem for the spherization of cotangent bundles, showing that Legendrian submanifolds with quadratic generating families remain so under isotopies.

Contribution

It establishes a new invariance result for Legendrian submanifolds in spherized cotangent bundles, extending Chekanov-type theorems.

Findings

Legendrian submanifolds with quadratic generating families are preserved under isotopies

The theorem applies to spherized cotangent bundles of closed manifolds

It generalizes known invariance results in contact topology

Abstract

We prove a Chekanov-type theorem for the spherization of the cotangent bundle $ST^*B$ of a closed manifold $B$. It claims that for Legendrian submanifolds in $ST^*B$ the property "to be given by a generating family quadratic at infinity" persists under Legendrian isotopies.