A FILTRATION ON EQUIVARIANT BOREL-MOORE HOMOLOGY

Creative Commons License

Bingham A., Can M. B., OZAN Y.

FORUM OF MATHEMATICS SIGMA, vol.7, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7
  • Publication Date: 2019
  • Doi Number: 10.1017/fms.2019.15
  • Journal Name: FORUM OF MATHEMATICS SIGMA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Middle East Technical University Affiliated: Yes

Abstract

Let G / H be a homogeneous variety and let X be a G-equivariant embedding of G / H such that the number of G-orbits in X is finite. We show that the equivariant Borel-Moore homology of X has a filtration with associated graded module the direct sum of the equivariant Borel-Moore homologies of the G-orbits. If T is a maximal torus of G such that each G-orbit has a T-fixed point, then the equivariant filtration descends to give a filtration on the ordinary Borel-Moore homology of X. We apply our findings to certain wonderful compactifications as well as to double flag varieties.