Negative Sasakian structures on simply-connected 5-manifolds

authored by

Vicente Muñoz, Matthias Schütt, Aleksy Tralle

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].

Organisation(s)

Institut für Algebraische Geometrie
Riemann Center for Geometry and Physics

External Organisation(s)

Universidad de Malaga
University of Warmia and Mazury

Type

Artikel

Journal

Mathematical research letters

Volume

29

Pages

1827-1857

No. of pages

31

ISSN

1073-2780

Publication date

04.05.2023

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Mathematik (insg.)

Electronic version(s)

https://doi.org/10.48550/arXiv.2007.08597 (Access: Offen)
https://doi.org/10.4310/MRL.2022.v29.n6.a9 (Access: Offen)