Rational smoothness, cellular decompositions and GKM theory

Gonzales, Richard

doi:10.2140/gt.2014.18.291

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Rational smoothness, cellular decompositions and GKM theory

Richard Gonzales

Geometry & Topology 18 (2014) 291–326

DOI: 10.2140/gt.2014.18.291

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

References

Publication

Received: 15 July 2012

Revised: 19 August 2013

Accepted: 20 September 2013

Published: 29 January 2014

Proposed: Frances Kirwan

Seconded: Leonid Polterovich, Yasha Eliashberg

Authors

Richard Gonzales
Faculty of Engineering and Natural Sciences Sabancı Üniversitesi Orhanli, Tuzla 34956 Istanbul Turkey

Volume 18, issue 1 (2014)