10 research outputs found
Pseudo-distances on symplectomorphism groups and applications to flux theory
Starting from a given norm on the vector space of exact 1-forms of a compact
symplectic manifold, we produce pseudo-distances on its symplectomorphism group
by generalizing an idea due to Banyaga. We prove that in some cases (which
include Banyaga's construction), their restriction to the Hamiltonian
diffeomorphism group is equivalent to the distance induced by the initial norm
on exact 1-forms. We also define genuine "distances to the Hamiltonian
diffeomorphism group" which we use to derive several consequences, mainly in
terms of flux groups.Comment: 21 pages, no figure; v2. various typos corrected, some references
added. Published in Mathematische Zeitschrif
Semisimplicity of the quantum cohomology for smooth Fano toric varieties associated with facet symmetric polytopes
The degree zero part of the quantum cohomology algebra of a smooth Fano toric
symplectic manifold is determined by the superpotential function, W, of its
moment polytope. In particular, this algebra is semisimple, i.e. splits as a
product of fields, if and only if all the critical points of W are
non-degenerate. In this paper we prove that this non-degeneracy holds for all
smooth Fano toric varieties with facet-symmetric duals to moment polytopes.Comment: 16 pages; corrected version, published in Electron. Res. Announc.
Math. Sc