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Kavli IPMU Komaba Seminar
Seminar information archive ～04/19｜Next seminar｜Future seminars 04/20～
| Date, time & place | Monday 16:30 - 18:00 002Room #002 (Graduate School of Math. Sci. Bldg.) |
|---|
2010/11/26
14:40-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)
Tomoo Matsumura (Cornell University)
Hamiltonian torus actions on orbifolds and orbifold-GKM theorem (joint
work with T. Holm) (JAPANESE)
Tomoo Matsumura (Cornell University)
Hamiltonian torus actions on orbifolds and orbifold-GKM theorem (joint
work with T. Holm) (JAPANESE)
[ Abstract ]
When a symplectic manifold M carries a Hamiltonian torus R action, the
injectivity theorem states that the R-equivariant cohomology of M is a
subring of the one of the fixed points and the GKM theorem allows us
to compute this subring by only using the data of 1-dimensional
orbits. The results in the first part of this talk are a
generalization of this technique to Hamiltonian R actions on orbifolds
and an application to the computation of the equivariant cohomology of
toric orbifolds. In the second part, we will introduce the equivariant
Chen-Ruan cohomology ring which is a symplectic invariant of the
action on the orbifold and explain the injectivity/GKM theorem for this ring.
When a symplectic manifold M carries a Hamiltonian torus R action, the
injectivity theorem states that the R-equivariant cohomology of M is a
subring of the one of the fixed points and the GKM theorem allows us
to compute this subring by only using the data of 1-dimensional
orbits. The results in the first part of this talk are a
generalization of this technique to Hamiltonian R actions on orbifolds
and an application to the computation of the equivariant cohomology of
toric orbifolds. In the second part, we will introduce the equivariant
Chen-Ruan cohomology ring which is a symplectic invariant of the
action on the orbifold and explain the injectivity/GKM theorem for this ring.
