The equivariant cohomology ring of regular varieties

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An introduction to equivariant cohomology and homology, following Goresky, Kottwitz, and MacPherson (2005, methodology): “xed points. GKM theory is used to calculate the equivariant cohomology rings of Grassmannians [KnTao] and regular varieties (which have a unique ﬁxed point with respect to a solvable group action) in [BC]. The graphs used in GKM theory are studied in their own right in [GuZ]. In order to make this e”
Exponents for B-stable ideals (2004, result): “We should mention that if one knew that Proposition 10.1 were true in all types then a result of Peterson announced in [ BC ] would be equivalent to Theorem 4.1.”
Paving Hessenberg varieties by affines (2007, result): “We understand D. Peterson has uncirculated results overlapping these [C], [ BC , Theorem 3]; we infer that the methods used here are substantively different.”
A positive Monk formula in the S1‐equivariant cohomology of type A Peterson varieties (2009, background): “Hessenberg varieties arise in many areas of mathematics, including geometric representation theory [12, 31, 33], numerical analysis [8], mathematical physics [24, 29], combinatorics [10], and algebraic geometry [5, 6, 34, 35].”