Geodesic
A FILTRATION ON EQUIVARIANT BOREL–MOORE HOMOLOGY
Forum of Mathematics, Sigma, Tome 7 (2019)

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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. 
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     author = {ARAM BINGHAM and MAHIR BILEN CAN and YILDIRAY OZAN},
     title = {A {FILTRATION} {ON} {EQUIVARIANT} {BOREL{\textendash}MOORE} {HOMOLOGY}},
     journal = {Forum of Mathematics, Sigma},
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     doi = {10.1017/fms.2019.15},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2019.15/}
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ARAM BINGHAM; MAHIR BILEN CAN; YILDIRAY OZAN. A FILTRATION ON EQUIVARIANT BOREL–MOORE HOMOLOGY. Forum of Mathematics, Sigma, Tome 7 (2019). doi: 10.1017/fms.2019.15

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