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Abstract
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Let
be a symplectic manifold, and
a closed connected symplectic
-manifold. We construct
a weakly symplectic form
on
which is a special case of Donaldson’s form. We show that the restriction
of
to any orbit of the group of Hamiltonian symplectomorphisms through a symplectic
embedding
descends to a weakly symplectic form on the quotient by
, and that the symplectic
space obtained is a symplectic quotient of the subspace of symplectic embeddings with respect to
the
-action. We also
compare
to another
-form. We conclude with a
result on the restriction of
to moduli spaces of holomorphic curves.
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Keywords
symplectic manifold, Donaldson's form, symplectic quotient,
moduli space of J-holomorphic curves
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Mathematical Subject Classification
Primary: 32Q60, 32Q65, 53D30, 53D35, 58B99
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Milestones
Received: 1 July 2019
Revised: 27 May 2021
Accepted: 27 November 2021
Published: 6 April 2022
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