A FILTRATION ON EQUIVARIANT BOREL-MOORE HOMOLOGY


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

FORUM OF MATHEMATICS SIGMA, cilt.7, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 7
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1017/fms.2019.15
  • Dergi Adı: FORUM OF MATHEMATICS SIGMA

Özet

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.