No symplectic-Lipschitz structures on $S^{2n \geq 4}$

TL;DR

This paper proves that spheres of dimension 4 and higher cannot have symplectic-Lipschitz structures, due to topological obstructions related to their cohomology groups.

Contribution

It establishes a topological obstruction to the existence of symplectic-Lipschitz structures on spheres of dimension 4 and higher.

Findings

Spheres $S^{2n}$ with $n extgreater 1$ do not admit symplectic-Lipschitz structures.

Manifolds with such structures must have non-vanishing even-degree cohomology groups.

The result links symplectic-Lipschitz structures to topological cohomology properties.

Abstract

We prove that a closed manifold which admits a symplectic-Lipschitz structure has non-vanishing even-degree cohomology groups with real coefficients. In particular, spheres $S^{2n}, n \geq 2$ do not admit symplectic-Lipschitz structures.