The positive fundamental group of $\mathrm{Sp}(2n)$

Abstract

In this paper, we examine the homotopy classes of positive loops in $\mathrm{Sp}(2n)$. We demonstrate that two positive loops are homotopic if and only if they are homotopic through positive loops. As consequences, we can extend several results of McDuff \cite{McD} and Chance \cite{Cha} to higher dimensional symplectic manifolds without dimensional restrictions.

55 pages, 18 figures, minor changes