On the sign ambiguity in equivariant cohomological rigidity of GKM graphs

Abstract

This is the sequel to the author’s previous paper [1] with Matthias Franz. In the present paper, we introduce the notion of equivariant total Chern class of a GKM graph and show that the pair of graph equivariant cohomology and the equivariant total Chern class determines the GKM graph completely. We also show that for a torus graph in the sense of Maeda–Masuda–Panov, the pair of graph equivariant cohomology and the equivariant 1-st Chern class determines the torus graph completely.