The Gromov-Tischler theorem for stratified spaces

TL;DR

This paper extends the Gromov-Tischler theorem to stratified spaces by defining symplectic structures on them and proving their embeddability into complex projective spaces with Kähler forms.

Contribution

It introduces a notion of symplectic structures on stratified spaces and proves their embeddability into projective spaces, generalizing a classical theorem from manifolds to stratified spaces.

Findings

Stratified spaces can admit symplectic structures with integral cohomology.

Such spaces can be embedded into complex projective spaces with standard Kähler forms.

The extension of Gromov-Tischler theorem to stratified spaces is established.

Abstract

We define a notion of a symplectic structure on stratified spaces, and demonstrate that given a symplectic structure on a stratified space $X$ with integral cohomology class, $X$ can be symplectically embedded in some complex projective space equipped with the standard K\"ahler form. This extends a theorem, due to Gromov and Tischler for manifolds, to stratified spaces.