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