تقرير
Quasi-regular Sasakian and K-contact structures on Smale-Barden manifolds
| العنوان: | Quasi-regular Sasakian and K-contact structures on Smale-Barden manifolds |
|---|---|
| المؤلفون: | Cañas, A., Muñoz, V., Schütt, M., Tralle, A. |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, Mathematics - Algebraic Geometry, Mathematics - Symplectic Geometry, 53C25, 53D35, 14J28, 14J17 |
| الوصف: | Smale-Barden manifolds are simply-connected closed 5-manifolds. It is an important and difficult question to decide when a Smale-Barden manifold admits a Sasakian or a K-contact structure. The known constructions of Sasakian and K-contact structures are obtained mainly by two techniques. These are either links (Boyer and Galicki), or semi-regular Seifert fibrations over smooth orbifolds (Koll\'ar). Recently, the second named author of this article started the systematic development of quasi-regular Seifert fibrations, that is, over orbifolds which are not necessarily smooth. The present work is devoted to several applications of this theory. First, we develop constructions of a Smale-Barden manifold admitting a quasi-regular Sasakian structure but not a semi-regular K-contact structure. Second, we determine all Smale-Barden manifolds that admit a null Sasakian structure. Finally, we show a counterexample in the realm of cyclic K\"ahler orbifolds to the algebro-geometric conjecture that claims that for an algebraic surface with $b_1=0$ and $b_2>1$ there cannot be $b_2$ smooth disjoint complex curves of genus g>0 spanning the (rational) homology. Comment: 23 pages, 1 figure |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2004.12643 |
| رقم الأكسشن: | edsarx.2004.12643 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |