Displaceability and the mean Euler characteristic

TL;DR

This paper demonstrates that the mean Euler characteristic of equivariant symplectic homology can obstruct displaceable exact contact embeddings, with applications to specific Brieskorn manifolds.

Contribution

It introduces a new obstruction criterion using the mean Euler characteristic for displaceability in contact geometry.

Findings

Mean Euler characteristic obstructs displaceable contact embeddings

Certain Brieskorn manifolds cannot admit displaceable embeddings

Provides new tools for contact topology analysis

Abstract

In this note we show that the mean Euler characteristic of equivariant symplectic homology is an effective obstruction against the existence of displaceable exact contact embeddings. As an application we show that certain Brieskorn manifolds do not admit displaceable exact contact embeddings.