Abstract
Lin and Sjamaar have used symplectic Hodge theory to obtain canonical equivariant extensions for Hamiltonian actions on closed symplectic manifolds that have the strong Lefschetz property. Here we obtain canonical equivariant extensions much more generally by means of classical Hodge theory.
Highlights
In [4], Lin and Sjamaar show how to use symplectic Hodge theory to obtain canonical equivariant extensions of closed forms in Hamiltonian actions of compact connected Lie groups on closed symplectic manifolds which have the strong Lefschetz property
We show how to do the same using classical Hodge theory
For nonabelian compact connected Lie groups, we use the small model, which is much simpler than the Cartan model and which has been shown to be chain homotopy equivalent to the Cartan model by Alekseev and Meinrenken
Summary
In [4], Lin and Sjamaar show how to use symplectic Hodge theory to obtain canonical equivariant extensions of closed forms in Hamiltonian actions of compact connected Lie groups on closed symplectic manifolds which have the strong Lefschetz property. We show how to do the same using classical Hodge theory. This has the advantage of applying far more generally. For nonabelian compact connected Lie groups, we use the small model, which is much simpler than the Cartan model and which has been shown to be chain homotopy equivalent to the Cartan model by Alekseev and Meinrenken (see [1]). The final section, considers the Cartan model
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