#### Volume 18, issue 1 (2014)

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Rational smoothness, cellular decompositions and GKM theory

### Richard Gonzales

Geometry & Topology 18 (2014) 291–326
##### Abstract

We introduce the notion of $ℚ$–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 $ℚ$–filtrable GKM variety. Applications to the theory of group embeddings are provided.

##### Keywords
rational smoothness, algebraic torus actions, GKM theory, equivariant cohomology, algebraic monoids, group embeddings
##### Mathematical Subject Classification 2010
Primary: 14F43, 14L30
Secondary: 55N91, 14M15