Rational smoothness, cellular decompositions and GKM theory

Abstract

We introduce the notion of $\mathbb{Q}$–filtrable varieties: projective varieties with a torus action and a finite number of fixed points, such that the cells of the associated Bialynicki-Birula decomposition are all rationally smooth. Our main results develop GKM theory in this setting. We also supply a method for building nice combinatorial bases on the equivariant cohomology of any $\mathbb{Q}$–filtrable GKM variety. Applications to the theory of group embeddings are provided.