Equivariant structure constants for ordinary and weighted projective space

Details Equivariant structure constants for ordinary and weighted projective space Equivariant structure constants for ordinary and weighted projective space

2008-06-22

arxiv.org/abs/0806.3588v1

Mathematics

Algebraic Topology

14 pages

Scientific paper

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 $\oplus_{i=0}^n \Z[t_1, t_2,..., t_n]$. 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.

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