辛群是N-确定的2-紧群

On symplectic vortex equations over a compact orbifold Riemann surface

Making use of theory of differentiable stacks, we study symplectic vortex equations over a compact orbifold Riemann surface. We discuss the category of representable morphisms from a compact orbifold Riemann surface to a quotient stack. After that we define symplectic vortex equations over a compact orbifold Riemann surface. We also discuss the moduli space of solutions to the equations for linear actions of the circle group on the complex plane.

辛Weiss演算

Symplectic Weiss calculi

本文提出两种辛Weiss演算，分别对应非紧与紧辛群，并证明前者收缩到酉演算，后者与其他版本比较并分类稳定平凡四元数向量丛。

具有Hamilton李群作用的辛流形的基本群

The fundamental group of symplectic manifolds with Hamiltonian Lie group actions

设$(M, ω)$是一个连通的紧辛流形，它具有一个Hamilton作用，其中$G$是一个连通的紧李群.让$ϕ$成为矩图。在\cite{L}中，我们证明了$G=S^1$作用的下列结果：作为拓扑空间的基本群，$π_1(M)=π_1(M_{red})$，其中$M_{red}$是矩映射$ϕ$在任意值处的辛商.本文将这一结果推广到其它连通紧李群的$G$作用.我们还证明了上述基本群与$M/G$的基本群同构。我们简要地讨论了第一部分的结果推广到非紧流形与适当的时刻映射。

Manifolds which are complex and symplectic but not Kähler

The first example of a compact manifold admitting both complex and symplectic structures but not admitting a Kähler structure is the renowned Kodaira-Thurston manifold. We review its construction and show that this paradigm is very general and is not related to the fundamental group. More specifically, we prove that the simply-connected $8$-dimensional compact manifold of [\textsc{M. Fernández and V. Muñoz}, \emph{An 8-dimensional non-formal simply connected symplectic manifold}, Ann. of Math. (2) \textbf{167}, no. 3, 1045--1054, 2008.] admits both symplectic and complex structures but does no…

6维辛流形上的半自由Hamilton圈作用

Semi-free Hamiltonian circle actions on 6 dimensional symplectic manifolds

假设$(M, ω)$是一个连通的、紧致的6维辛流形，它具有一个半自由的Hamilton圈作用，使得不动点集由孤立点或紧致的可定向曲面组成。我们将注意力限制在$\dim$ $H^2(M)<3$病例上。给出了可能流形的完整列表，确定了它们的等变上同调环和等变Chern类。这些流形中的一些被分类为单同态。我们还证明了一些情况下的存在性。

一个8维非形式simply connected辛流形

An 8-dimensional non-formal simply connected symplectic manifold

构造了一个8维非形式单连通紧致辛流形。