The Atiyah-Guillemin-Sternberg theorem says that the image of a moment map of a toric action is independent of the choice of symplectic form in the cohomology class. So all is well for a smooth symplectic form in the same cohomology class. My question is whether we can extend this to the case when the symplectic form is singular, e.g. when the manifold is Kahler and the symplectic form is just a current. How can we define the Hamiltonian function for the toric action?
$\begingroup$
$\endgroup$
7
-
$\begingroup$ cohomology in current setting doesn't change and is as same as form $\endgroup$– user21574Commented May 1, 2016 at 3:06
-
$\begingroup$ mathoverflow.net/questions/85399/cohomology-class-of-a-current $\endgroup$– user21574Commented May 1, 2016 at 3:10
-
$\begingroup$ Thanks! The cohomology is almost the same as for the form. But the definition of moment map is always for the smooth symplectic form. I wonder whether it can be extended to the current. $\endgroup$– DanielCommented May 1, 2016 at 3:59
-
$\begingroup$ You can assume symplectic quotient as stratified space in singular setting. $\endgroup$– user21574Commented May 1, 2016 at 4:31
-
$\begingroup$ math.cornell.edu/~sjamaar/papers/stratified.pdf I read this paper 4 years ago. $\endgroup$– user21574Commented May 1, 2016 at 4:32
|
Show 2 more comments