## Towards Generalizing Schubert Calculus in the Symplectic Category

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 fixed… Expand

## The Cohomology Ring of Weight Varieties and Polygon Spaces

- R. Goldin
- Mathematics
- 25 June 2001

We use a theorem of S. Tolman and J. Weitsman (The cohomology rings of Abelian symplectic quotients, math. DG/9807173) to find explicit formulae for the rational cohomology rings of the symplectic… Expand

## An effective algorithm for the cohomology ring of symplectic reductions

- R. Goldin
- Mathematics
- 1 October 2001

Abstract. Let G be a compact torus acting on a compact symplectic manifold M in a Hamiltonian fashion, and T a subtorus of G. We prove that the kernel of $ \kappa : H^\ast_G(M) \to H^\ast(M//G) $ is… Expand

## Orbifold cohomology of torus quotients

- R. Goldin, T. Holm, A. Knutson
- Mathematics
- 20 February 2005

We introduce the_inertial cohomology ring_ NH^*_T(Y) of a stably almost complex manifold carrying an action of a torus T. We show that in the case that Y has a locally free action by T, the inertial… Expand

## ORBIFOLD COHOMOLOGY OF HYPERTORIC VARIETIES

Hypertoric varieties are hyperkahler analogues of toric varieties, and are constructed as abelian hyperkahler quotients T*ℂn//// T of a quaternionic affine space. Just as symplectic toric orbifolds… Expand

## Cohomology Pairings on the Symplectic Reduction of Products

Abstract 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… Expand

## Resolving Singularities of Plane Analytic Branches with one Toric Morphism

- R. Goldin, B. Teissier
- Mathematics
- 2000

Let (C, 0) be an irreducible germ of complex plane curve. Let Γ ⊂ ℕ be the semigroup associated to it and C Γ ⊂ ℂ g+1 the corresponding monomial curve, where g is the number of Puiseux exponents of… Expand

## Torsion in the full orbifold K-theory of abelian symplectic quotients

Let (M, ω, Φ) be a Hamiltonian T-space and let $${H\subseteq T}$$ be a closed Lie subtorus. Under some technical hypotheses on the moment map Φ, we prove that there is no additive torsion in the… Expand

## Real loci of symplectic reductions

Let M be a compact, connected symplectic manifold with a Hamiltonian action of a compact n-dimensional torus T. Suppose that M is equipped with an anti-symplectic involution a compatible with the… Expand

## Torsion in the full orbifold K-theory of abelian symplectic quotients

Let (M, ω, Φ) be a Hamiltonian T-space and let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}… Expand

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