Symplectic action around loops in $\text{Ham}(M)$

Mathematics – Symplectic Geometry

Scientific paper

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Expanded version. To appear in Geometriae Dedicata

Scientific paper

Let $\text{Ham(M)}$ be the group of Hamiltonian symplectomorphisms of a
quantizable, compact, symplectic manifold $(M,\omega)$. We prove the existence
of an action integral around loops in $\text{Ham(M)}$, and determine the value
of this action integral on particular loops when the manifold is a coadjoint
orbit.

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