Hearing Delzant polytopes from the equivariant spectrum

Details Hearing Delzant polytopes from the equivariant spectrum Hearing Delzant polytopes from the equivariant spectrum

2009-08-05

arxiv.org/abs/0908.0727v1

Mathematics

Differential Geometry

23 pages, 9 figures

Scientific paper

Let M^{2n} be a symplectic toric manifold with a fixed T^n-action and with a toric K\"ahler metric g. Abreu asked whether the spectrum of the Laplace operator $\Delta_g$ on $\mathcal{C}^\infty(M)$ determines the moment polytope of M, and hence by Delzant's theorem determines M up to symplectomorphism. We report on some progress made on an equivariant version of this conjecture. If the moment polygon of M^4 is generic and does not have too many pairs of parallel sides, the so-called equivariant spectrum of M and the spectrum of its associated real manifold M_R determine its polygon, up to translation and a small number of choices. For M of arbitrary even dimension and with integer cohomology class, the equivariant spectrum of the Laplacian acting on sections of a naturally associated line bundle determines the moment polytope of M.

Affiliated with

Also associated with

No associations

Rating

Hearing Delzant polytopes from the equivariant spectrum does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hearing Delzant polytopes from the equivariant spectrum, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hearing Delzant polytopes from the equivariant spectrum will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-705307