Atiyah-Bott localization in equivariant Witt cohomology
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916604665659392 |
|---|---|
| author | Levine, Marc |
| author_facet | Levine, Marc |
| contents | Let $N$ be a normalizer of the diagonal torus $T_1\cong \mathbb{G}_m$ in $\text{SL}_2$. We prove localization theorems for $\text{SL}_2^n$ and $N^n$ for equivariant cohomology with coefficients in the (twisted) Witt sheaf, along the lines of the classical Atiyah-Bott localization theorems for equivariant cohomology for a torus action. We also have an analog of the Bott residue formula for $\text{SL}_2^n$ and $N$. In the case of an $\text{SL}_2^n$-action, there is a rather serious restriction on the orbit type. For an $N$-action, there is no restriction for the localization result, but for the Bott residue theorem, one requires a certain type of decomposition of the fixed points for the $T_1$-action. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_13882 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Atiyah-Bott localization in equivariant Witt cohomology Levine, Marc Algebraic Geometry Algebraic Topology 14F42 Let $N$ be a normalizer of the diagonal torus $T_1\cong \mathbb{G}_m$ in $\text{SL}_2$. We prove localization theorems for $\text{SL}_2^n$ and $N^n$ for equivariant cohomology with coefficients in the (twisted) Witt sheaf, along the lines of the classical Atiyah-Bott localization theorems for equivariant cohomology for a torus action. We also have an analog of the Bott residue formula for $\text{SL}_2^n$ and $N$. In the case of an $\text{SL}_2^n$-action, there is a rather serious restriction on the orbit type. For an $N$-action, there is no restriction for the localization result, but for the Bott residue theorem, one requires a certain type of decomposition of the fixed points for the $T_1$-action. |
| title | Atiyah-Bott localization in equivariant Witt cohomology |
| topic | Algebraic Geometry Algebraic Topology 14F42 |
| url | https://arxiv.org/abs/2203.13882 |