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A FILTRATION ON EQUIVARIANT BOREL–MOORE HOMOLOGY

Published online by Cambridge University Press:  04 July 2019

ARAM BINGHAM
Affiliation:
Department of Mathematics, Tulane University, New Orleans, 70118, LA, USA; abingham@tulane.edu, mahirbilencan@gmail.com
MAHIR BILEN CAN
Affiliation:
Department of Mathematics, Tulane University, New Orleans, 70118, LA, USA; abingham@tulane.edu, mahirbilencan@gmail.com
YILDIRAY OZAN
Affiliation:
Department of Mathematics, Middle East Technical University, Ankara, Turkey; ozan@metu.edu.tr

Abstract

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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.

Type
Research Article
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2019

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