An exotic symplectic $\mathbf{R}^6$

TL;DR

This paper constructs explicit examples of exotic symplectic structures on Euclidean spaces of dimensions 4 and 6, extending to all even dimensions greater than or equal to 4, thus providing concrete instances of such structures.

Contribution

It provides explicit examples of exotic symplectic forms on n for all n, including the first explicit example in 6.

Findings

Explicit exotic symplectic 6 constructed.

Extension of examples to all n for n.

Advances understanding of symplectic topology in Euclidean spaces.

Abstract

An explicit example of an exotic symplectic $\mathbf{R}^6$ is given. Together with an earlier known example on $\mathbf{R}^4$, this yields an explicit exotic symplectic form on $\mathbf{R}^{2n}$ for all $n\geq2$.