无半正则sasaki结构的k接触单连通5流形

IF 0.8 3区数学 Q2 MATHEMATICS

Publicacions Matematiques Pub Date : 2020-11-01 DOI:10.5565/PUBLMAT6522107

Alejandro Cañas, V. Muñoz, J. Rojo, A. Viruel

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引用次数: 2

摘要

我们构造了一个5维单连通紧致流形的第一个例子，它允许K接触结构，但不允许半正则Sasakian结构。为此，我们需要两个成分：（a）构造一个合适的具有跨越同调的不相交辛表面的单连通辛4-流形，除了亏格1中的一个和亏格g>1中的另一个，（b）证明了$b_1=0$代数曲面的第二个Betti数$b_2$上的一个界，当除一个为亏格1，另一个为g>1时，该代数曲面具有跨越同调的不相交复曲线。

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A K-contact simply connected 5-manifold with no semi-regular Sasakian structure

We construct the first example of a 5-dimensional simply connected compact manifold that admits a K-contact structure but does not admit a semi-regular Sasakian structure. For this, we need two ingredients: (a) to construct a suitable simply connected symplectic 4-manifold with disjoint symplectic surfaces spanning the homology, all of them but one of genus 1 and the other of genus g>1, (b) to prove a bound on the second Betti number $b_2$ of an algebraic surface with $b_1=0$ and having disjoint complex curves spanning the homology when all of them but one are of genus 1 and the other of genus g>1.

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来源期刊

Publicacions Matematiques 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publicacions Matemàtiques is a research mathematical journal published by the Department of Mathematics of the Universitat Autònoma de Barcelona since 1976 (before 1988 named Publicacions de la Secció de Matemàtiques, ISSN: 0210-2978 print, 2014-4369 online). Two issues, constituting a single volume, are published each year. The journal has a large circulation being received by more than two hundred libraries all over the world. It is indexed by Mathematical Reviews, Zentralblatt Math., Science Citation Index, SciSearch®, ISI Alerting Services, COMPUMATH Citation Index®, and it participates in the Euclid Project and JSTOR. Free access is provided to all published papers through the web page. Publicacions Matemàtiques is a non-profit university journal which gives special attention to the authors during the whole editorial process. In 2019, the average time between the reception of a paper and its publication was twenty-two months, and the average time between the acceptance of a paper and its publication was fifteen months. The journal keeps on receiving a large number of submissions, so the authors should be warned that currently only articles with excellent reports can be accepted.