Equivariant triple intersections

Triple Intersections and Geometric Transitions

The local neighborhood of a triple intersection of fivebranes in type IIA string theory is shown to be equivalent to type IIB string theory on a noncompact Calabi-Yau fourfold. The phases and the effective theory of the intersection are analyzed in detail.

Pieri-type Formulas for Maximal Isotropic Grassmannians via Triple Intersections

We give an elementary proof of the Pieri-type formula in the cohomology of a Grassmannian of maximal isotropic subspaces of an odd orthogonal or symplectic vector space. This proof proceeds by explicitly computing a triple intersection of Schubert varieties. The decisive step is an exact description of the intersection of two Schubert varieties, from which the multiplicities (which are powers o...

Regularity and dimension spectrum of the equivariant spectral triple for the odd dimensional quantum spheres

The odd dimensional quantum sphere S q is a homogeneous space for the quantum group SUq(l + 1). A generic equivariant spectral triple for S 2l+1 q on its L2 space was constructed by Chakraborty & Pal in [4]. We prove regularity for that spectral triple here. We also compute its dimension spectrum and show that it is simple. We give detailed construction of its smooth function algebra and some r...

Laws of the Iterated Logarithm for Triple Intersections of RandomWalks on Z

Equivariant cohomology and equivariant intersection theory

This text is an introduction to equivariant cohomology, a classical tool for topological transformation groups, and to equivariant intersection theory, a much more recent topic initiated by D. Edidin and W. Graham. It is based on lectures given at Montréal is Summer 1997. Our main aim is to obtain explicit descriptions of cohomology or Chow rings of certain manifolds with group actions which ar...