A FILTRATION ON EQUIVARIANT BOREL–MOORE HOMOLOGY
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...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2019-01-01
|
| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S205050941900015X/type/journal_article |
| _version_ | 1811156190299684864 |
|---|---|
| author | ARAM BINGHAM MAHIR BILEN CAN YILDIRAY OZAN |
| author_facet | ARAM BINGHAM MAHIR BILEN CAN YILDIRAY OZAN |
| author_sort | ARAM BINGHAM |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-10T04:47:22Z |
| format | Article |
| id | doaj.art-a4aa72282cd24023a9fe26f6310feb46 |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-04-10T04:47:22Z |
| publishDate | 2019-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-a4aa72282cd24023a9fe26f6310feb462023-03-09T12:34:44ZengCambridge University PressForum of Mathematics, Sigma2050-50942019-01-01710.1017/fms.2019.15A FILTRATION ON EQUIVARIANT BOREL–MOORE HOMOLOGYARAM BINGHAM0MAHIR BILEN CAN1https://orcid.org/0000-0002-0175-4897YILDIRAY OZAN2Department of Mathematics, Tulane University, New Orleans, 70118, LA, USA; ,Department of Mathematics, Tulane University, New Orleans, 70118, LA, USA; ,Department of Mathematics, Middle East Technical University, Ankara, Turkey;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.https://www.cambridge.org/core/product/identifier/S205050941900015X/type/journal_article14C15 (primary)14M27 (secondary) |
| spellingShingle | ARAM BINGHAM MAHIR BILEN CAN YILDIRAY OZAN A FILTRATION ON EQUIVARIANT BOREL–MOORE HOMOLOGY Forum of Mathematics, Sigma 14C15 (primary) 14M27 (secondary) |
| title | A FILTRATION ON EQUIVARIANT BOREL–MOORE HOMOLOGY |
| title_full | A FILTRATION ON EQUIVARIANT BOREL–MOORE HOMOLOGY |
| title_fullStr | A FILTRATION ON EQUIVARIANT BOREL–MOORE HOMOLOGY |
| title_full_unstemmed | A FILTRATION ON EQUIVARIANT BOREL–MOORE HOMOLOGY |
| title_short | A FILTRATION ON EQUIVARIANT BOREL–MOORE HOMOLOGY |
| title_sort | filtration on equivariant borel moore homology |
| topic | 14C15 (primary) 14M27 (secondary) |
| url | https://www.cambridge.org/core/product/identifier/S205050941900015X/type/journal_article |
| work_keys_str_mv | AT arambingham afiltrationonequivariantborelmoorehomology AT mahirbilencan afiltrationonequivariantborelmoorehomology AT yildirayozan afiltrationonequivariantborelmoorehomology AT arambingham filtrationonequivariantborelmoorehomology AT mahirbilencan filtrationonequivariantborelmoorehomology AT yildirayozan filtrationonequivariantborelmoorehomology |