A filtration on equivariant Borel-Moore homology

Bingham, Aram
Can, Mahir Bilen
Ozan, Yıldıray
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.

Citation Formats
A. Bingham, M. B. Can, and Y. Ozan, “A filtration on equivariant Borel-Moore homology,” FORUM OF MATHEMATICS SIGMA, vol. 7, pp. 0–0, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32907.