Equivariant structure constants for Hamiltonian-$T$-spaces

TL;DR

This paper derives formulas for equivariant structure constants in Hamiltonian-$T$-spaces with canonical classes, generalizing Tymoczko's results and providing new computational tools in equivariant cohomology.

Contribution

It introduces formulas for structure constants in Hamiltonian-$T$-spaces with canonical classes, extending Tymoczko's work.

Findings

Formulas relate structure constants to fixed point data

Generalization of Tymoczko's results

Provides computational methods for equivariant cohomology

Abstract

If there exists a set of canonical classes on a compact Hamiltonian-$T$-spaces in the sense of Goldin and Tolman, we derive some formulas for certain equivariant structure constants in terms of other equivariant structure constants and the values of canonical classes restricted to some fixed points. These formulas can be regarded as a generalization of Tymoczko's results.