Equivariant structure constants for ordinary and weighted projective space

2008/06/22 by Tymoczko, Julianna S.
#05E15 (Primary) #14M15 (Secondary) #55N91 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.0806.3588

Abstract

We compute the integral torus-equivariant cohomology ring for weighted projective space for two different torus actions by embedding the cohomology in a sum of polynomial rings ⊕_i=0ⁿ \Z[t₁, t₂,..., t_n]. One torus action gives a result complementing that of Bahri, Franz, and Ray. For the other torus action, each basis class for weighted projective space is a multiple of the basis class for ordinary projective space; we identify each multiple explicitly. We also give a simple formula for the structure constants of the equivariant cohomology ring of ordinary projective space in terms of the basis of Schubert classes, as a sequence of divided difference operators applied to a specific polynomial.

Related

• Equivariant Cohomology of Weighted Grassmannians and Weighted Schubert Classes
• Three presentations of torus equivariant cohomology of flag manifolds
• The equivariant K-theory and cobordism rings of divisive weighted projective spaces
• Structure Constants in equivariant oriented cohomology of flag varieties
• Equivariant Cohomology of Projective Spaces