Weinstein neighbourhood theorems for stratified subspaces

TL;DR

This paper extends Weinstein's neighbourhood theorem to stratified subspaces, establishing uniqueness results and new tubular neighbourhood theorems, which aid in the study of exotic Lagrangians and symplectic geometry.

Contribution

It introduces a generalized Weinstein neighbourhood theorem for stratified subspaces, including a strong Moser's trick and a tubular neighbourhood theorem, broadening symplectic geometric tools.

Findings

Proved a uniqueness result for symplectic neighbourhoods of stratified subspaces.

Established a strong version of Moser's trick applicable to stratified contexts.

Developed a non-symplectic tubular neighbourhood theorem for stratified subspaces.

Abstract

By analogy with Weinstein's neighbourhood theorem, we prove a uniqueness result for symplectic neighbourhoods of a large family of stratified subspaces. This result generalizes existing constructions, e.g., in the search for exotic Lagrangians. Along the way, we prove a strong version of Moser's trick and a (non-symplectic) tubular neighbourhood theorem for these stratified subspaces.