Borel-Hirzebruch type formula for the graph equivariant cohomology of a projective bundle over a GKM-graph
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915328988020736 |
|---|---|
| author | Kuroki, Shintaro Solomadin, Grigory |
| author_facet | Kuroki, Shintaro Solomadin, Grigory |
| contents | In this paper, we introduce the GKM theoretical counterpart of the equivariant complex vector bundles as the "leg bundle". We also provide a definition for the projectivization of a leg bundle and prove the Borel-Hirzebruch type formula for its graph equivariant cohomology, assuming that the projectivization is again a GKM graph. Furthermore, we study the realization of the projective GKM fiber bundle, in the sense of Guillemin-Sabatini-Zara, can be obtained from the projectivization of a leg bundle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_11380 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Borel-Hirzebruch type formula for the graph equivariant cohomology of a projective bundle over a GKM-graph Kuroki, Shintaro Solomadin, Grigory Algebraic Topology Combinatorics In this paper, we introduce the GKM theoretical counterpart of the equivariant complex vector bundles as the "leg bundle". We also provide a definition for the projectivization of a leg bundle and prove the Borel-Hirzebruch type formula for its graph equivariant cohomology, assuming that the projectivization is again a GKM graph. Furthermore, we study the realization of the projective GKM fiber bundle, in the sense of Guillemin-Sabatini-Zara, can be obtained from the projectivization of a leg bundle. |
| title | Borel-Hirzebruch type formula for the graph equivariant cohomology of a projective bundle over a GKM-graph |
| topic | Algebraic Topology Combinatorics |
| url | https://arxiv.org/abs/2207.11380 |