Hard Lefschetz property for $\mathbb{S}^3$-actions
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929698457518080 |
|---|---|
| author | Prieto, JosÉ Ignacio Royo Saralegi-Aranguren, Martintxo Wolak, Robert |
| author_facet | Prieto, JosÉ Ignacio Royo Saralegi-Aranguren, Martintxo Wolak, Robert |
| contents | The Hard Lefschetz Property (HLP) has recently been formulated in the context of isometric flows without singularities on manifolds. In this category, two versions of the HLP (transverse and not) have been proven to be equivalent, thus generalizing what happens in the important cases of both K-contact and Sasakian manifolds. In this work we define both versions of the HLP for almost-free S3 -actions, and prove that they agree for actions satisfying a cohomological condition, which includes the important category of 3-Sasakian manifolds, where those two versions of the HLP are shown to be held. We also provide a family of examples of free actions of the 3-sphere which are not 3-Sasakian manifolds, but satisfy the HLP. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_00466 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hard Lefschetz property for $\mathbb{S}^3$-actions Prieto, JosÉ Ignacio Royo Saralegi-Aranguren, Martintxo Wolak, Robert Differential Geometry 53C25 (Primary), 37C85, 58D19 (secondary) The Hard Lefschetz Property (HLP) has recently been formulated in the context of isometric flows without singularities on manifolds. In this category, two versions of the HLP (transverse and not) have been proven to be equivalent, thus generalizing what happens in the important cases of both K-contact and Sasakian manifolds. In this work we define both versions of the HLP for almost-free S3 -actions, and prove that they agree for actions satisfying a cohomological condition, which includes the important category of 3-Sasakian manifolds, where those two versions of the HLP are shown to be held. We also provide a family of examples of free actions of the 3-sphere which are not 3-Sasakian manifolds, but satisfy the HLP. |
| title | Hard Lefschetz property for $\mathbb{S}^3$-actions |
| topic | Differential Geometry 53C25 (Primary), 37C85, 58D19 (secondary) |
| url | https://arxiv.org/abs/2310.00466 |