I have another short question regarding terminology. The phonetic similarity of simplex and symplectic manifold has little or nothing to do with any mathematical relationship, correct?
I always considered a symplectic manifold to be a smooth manifold with an associated two form and a simplex to be a generalized tetrahedron. In conversation, someone asked me if any relationship existed between them, and I responded that there was none of which I was aware. I wanted to see if anyone could offer a potential connection or validate the absence of one.
Thank you all.