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The positive fundamental group of ${\rm Sp}(2n)$
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classification
math.SG
keywords
positiveloopscitedimensionalhomotopicchanceclassesconsequences
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abstract
In this paper, we examine the homotopy classes of positive loops in ${\rm Sp}(2n)$. 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.
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