Details
| Original language | English |
|---|---|
| Pages (from-to) | 1827-1857 |
| Number of pages | 31 |
| Journal | Mathematical research letters |
| Volume | 29 |
| Issue number | 6 |
| Publication status | Published - 4 May 2023 |
Abstract
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In: Mathematical research letters, Vol. 29, No. 6, 04.05.2023, p. 1827-1857.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Negative Sasakian structures on simply-connected 5-manifolds
AU - Muñoz, Vicente
AU - Schütt, Matthias
AU - Tralle, Aleksy
N1 - Funding Information: The first author was partially supported by Project MINECO (Spain) PGC2018-095448-B-I00. The third author was supported by the National Science Center (Poland), grant. no. 2018/31/B/ST1/00053
PY - 2023/5/4
Y1 - 2023/5/4
N2 - 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].
AB - 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].
KW - math.DG
KW - math.AG
KW - math.SG
UR - http://www.scopus.com/inward/record.url?scp=85162787433&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2007.08597
DO - 10.48550/arXiv.2007.08597
M3 - Article
VL - 29
SP - 1827
EP - 1857
JO - Mathematical research letters
JF - Mathematical research letters
SN - 1073-2780
IS - 6
ER -