A note on the front spinning construction

TL;DR

This paper introduces a generalized front S^m-spinning construction for Legendrian submanifolds, demonstrating the existence of infinitely many Legendrian spheres with identical classical invariants that are not Legendrian isotopic.

Contribution

It extends the front S^1-spinning concept to higher dimensions and proves the existence of infinitely many Legendrian spheres with the same classical invariants that are not Legendrian isotopic.

Findings

Infinite pairs of Legendrian spheres are shown to be Legendrian cobordant but not isotopic.

The construction applies to spheres with at least one odd-dimensional factor.

Classical invariants are insufficient to distinguish these Legendrian submanifolds.

Abstract

In this paper we introduce a notion of front S^m-spinning for Legendrian submanifolds of R^{2n+1}. It generalizes the notion of front S^1-spinning which was invented by Ekholm, Etnyre and Sullivan. We use it to prove that there are infinitely many pairs of exact Lagrangian cobordant and not pairwise Legendrian isotopic Legendrian S^1 x S^{i_1} x ... x S^{i_k} in the standard contact Euclidean space which have the same classical invariants if one of i_j's is odd.