Gompf connected sum for orbifolds and K-contact Smale-Barden manifolds

Homology Smale-Barden manifolds with K-contact and Sasakian structures

Kollár has found subtle obstructions to the existence of Sasakian structures on 5-dimensional manifolds. In the present article we develop methods of using these obstructions to distinguish K-contact manifolds from Sasakian ones. In particular, we find the first example of a closed 5-manifold M with $H_1(M,Z)=0$ which is K-contact but which carries no semi-regular Sasakian structures.

Quasi-regular Sasakian and K-contact structures on Smale-Barden manifolds

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 (Kollár). 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 …

一个允许 K-contact 但不允许 Sasakian 结构的 Smale-Barden 流形

A Smale-Barden manifold admitting K-contact but not Sasakian structure

本文构造了首个允许 K-contact 结构却不存在任何 Sasakian 结构的单连通紧 5 维 Smale-Barden 流形，解决了 Boyer 与 Galicki 的长期问题。

关于K-接触非Sasakian Smale-Barden流形的构造

On the construction of K-contact non-Sasakian Smale-Barden manifolds

本文澄清并推广了构造首个单连通紧致5维K-接触非Sasakian Smale-Barden流形的方法，确定了所需的辛曲面数量，并推广了辛4-流形中具有横截交的辛曲面构造以分析地理问题。

On the classification of Smale-Barden manifolds with Sasakian structures

Smale-Barden manifolds $M$ are classified by their second homology $H_2(M,{\mathbb Z})$ and the Barden invariant $i(M)$. It is an important and dificult question to decide when $M$ admits a Sasakian structure in terms of these data. In this work we show methods of doing this. In particular we realize all $M$ with $H_2(M)={\mathbb Z}^k\oplus(\oplus_{i=1}^r{\mathbb Z}_{m_i}^{2g_i})$ and $i=0,\infty$, provided that $k\geq 1$, $m_i\geq 2$, $g_i\geq 1$, $m_i$ are pairwise coprime. Using our methods we also contribute to the problem of the existence of definite Sasakian structures on rational homolo…

具有横截交点的辛4维流形中辛曲面的构造

Constructions of symplectic surfaces in symplectic 4-manifolds with transversal intersections

本文修订、改进并推广辛4维流形中带横截交点的辛曲面构造，以支撑辛4轨形上Seifert丛分歧轨迹及非Sasakian的K-contact 5维流形构造。