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A Filtration on Equivariant Borel-Moore Homology

2018/09/10 by Bingham, Aram, Can, Mahir Bilen, Ozan, Yıldıray
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.03226

Abstract

Let G/H be a homogeneous variety, and let X be a G-equivariant embedding of G/Hsuch 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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