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

Jian Wang; Qinglong Zhou

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The positive fundamental group of {rm Sp}(2n)

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arxiv 2405.07398 v4 pith:WL2TNMGZ submitted 2024-05-12 math.SG

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

Jian Wang , Qinglong Zhou This is my paper

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.

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

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