A Filtration on Equivariant Borel-Moore Homology

Aram Bingham; Mahir Bilen Can; Yıldıray Ozan

A Filtration on Equivariant Borel-Moore Homology

Algebraic Geometry 2019-06-06 v2 Algebraic Topology

Authors: Aram Bingham , Mahir Bilen Can , Yıldıray Ozan

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.

Keywords

equivariant borel-moore homology filtration homogeneous variety g-orbits maximal torus wonderful compactifications double flag varieties

Cite

@article{arxiv.1809.03226,
  title  = {A Filtration on Equivariant Borel-Moore Homology},
  author = {Aram Bingham and Mahir Bilen Can and Yıldıray Ozan},
  journal= {arXiv preprint arXiv:1809.03226},
  year   = {2019}
}

Comments

The article is significantly shortened and an application is included. This version is to appear in Forum of Mathematics, Sigma

A Filtration on Equivariant Borel-Moore Homology

Abstract

Keywords

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