Cohomology of type $B$ real permutohedral varieties
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915939723771904 |
|---|---|
| author | Yoon, Younghan |
| author_facet | Yoon, Younghan |
| contents | Type $A$ and type $B$ permutohedral varieties are classic examples of mathematics, and their topological invariants are well known. This naturally leads to the investigation of the topology of their real loci, known as type $A$ and type $B$ real permutohedral varieties.
The rational cohomology rings of type $A$ real permutohedral varieties are fully described in terms of alternating permutations. Until now, only rational Betti numbers of type $B$ real permutohedral varieties have been described in terms of $B$-snakes. In this paper, we explicitly describe the multiplicative structure of the cohomology rings of type $B$ real permutohedral varieties in terms of $B$-snakes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09496 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cohomology of type $B$ real permutohedral varieties Yoon, Younghan Algebraic Topology Algebraic Geometry Combinatorics 57S12, 14P25, 14M25, 55U10, 20F55 Type $A$ and type $B$ permutohedral varieties are classic examples of mathematics, and their topological invariants are well known. This naturally leads to the investigation of the topology of their real loci, known as type $A$ and type $B$ real permutohedral varieties. The rational cohomology rings of type $A$ real permutohedral varieties are fully described in terms of alternating permutations. Until now, only rational Betti numbers of type $B$ real permutohedral varieties have been described in terms of $B$-snakes. In this paper, we explicitly describe the multiplicative structure of the cohomology rings of type $B$ real permutohedral varieties in terms of $B$-snakes. |
| title | Cohomology of type $B$ real permutohedral varieties |
| topic | Algebraic Topology Algebraic Geometry Combinatorics 57S12, 14P25, 14M25, 55U10, 20F55 |
| url | https://arxiv.org/abs/2501.09496 |