Let G be a compact torus acting on a compact sym-plectic manifold M in a Hamiltonian fashion, and T a subtorus of G. We prove that the kernel of Îº : H * G (M) â†’ H * (M//G) is generated by a smallâ€¦ (More)

Let (C; 0) be an irreducible germ of complex plane curve. Let ? N be the semigroup associated to it and C ? C g+1 the corresponding monomial curve, where g is the number of Puiseux exponents of (C;â€¦ (More)

The main purpose of this article is to extend some of the ideas from Schubert calculus to the more general setting of Hamiltonian torus actions on compact symplectic manifolds with isolated fixedâ€¦ (More)

Of fundamental importance in describing a neuronâ€™s activity and constructing biologically plausible neural networks is the unambiguous description of its smallest element of input in the integrationâ€¦ (More)

The notion of a universal semantic cognitive map is introduced as a general indexing space for semantics, useful to reduce semantic relations to geometric and topological relations. As a first stepâ€¦ (More)

We use a theorem of Tolman and Weitsman [23] to find explicit formulÃ¦ for the rational cohomology rings of the symplectic reduction of flag varieties in C, or generic coadjoint orbits of SU(n), byâ€¦ (More)

We show that for a Hamiltonian action of a compact torus G on a compact, connected symplectic manifold M , the G-equivariant cohomology is determined by the residual S 1 action on the submanifolds ofâ€¦ (More)

Hypertoric varieties are hyperkÃ¤hler analogues of toric varieties, and are constructed as abelian hyperkÃ¤hler quotients T C////T of a quaternionic affine space. Just as symplectic toric orbifolds areâ€¦ (More)

Let M be the product of two compact Hamiltonian T-spaces X and Y. We present a formula for evaluating integrals on the symplectic reduction of M by the diagonal T action. At every regular value ofâ€¦ (More)

We describe the cohomology ring of the symplectic reductions by tori of coadjoint orbits, or weight varieties. Weight varieties arise from representation theory considerations, and are temed as suchâ€¦ (More)