A filtration on equivariant Borel-Moore homology

Date

2019-07-04

Author

Bingham, Aram
Can, Mahir Bilen
Ozan, Yıldıray

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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.

URI

https://hdl.handle.net/11511/32907

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Department of Mathematics, Article