Publications at the Riemann Center
Negative Sasakian structures on simply-connected 5-manifolds
Abstract
We study several questions on the existence of negative Sasakian structures on simply connected rational homology spheres and on Smale-Barden manifolds of the form \(\#_k(S^2\times S^3)\). First, we prove that any simply connected rational homology sphere admitting positive Sasakian structures also admits a negative one. This result answers the question, posed by Boyer and Galicki in their book [BG], of determining which simply connected rational homology spheres admit both negative and positive Sasakian structures. Second, we prove that the connected sum \(\#_k(S^2\times S^3)\) admits negative quasi-regular Sasakian structures for any \(k\). This yields a complete answer to another question posed in [BG].
Details
- Organisation(s)
-
Institute of Algebraic Geometry
Riemann Center for Geometry and Physics
- External Organisation(s)
-
Universidad de Malaga
University of Warmia and Mazury
- Type
- Article
- Journal
- Mathematical research letters
- Volume
- 29
- Pages
- 1827-1857
- No. of pages
- 31
- ISSN
- 1073-2780
- Publication date
- 04.05.2023
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- General Mathematics
- Electronic version(s)
-
https://doi.org/10.48550/arXiv.2007.08597 (Access:
Open
)
https://doi.org/10.4310/MRL.2022.v29.n6.a9 (Access: Open )
