Link Obstruction to Riemannian smoothings of locally CAT(0) 4-manifolds

4-流形中拓扑曲面的灯泡光滑化

Light bulb smoothing for topological surfaces in 4-manifolds

本文提出4-流形中拓扑嵌入曲面的新光滑化技术，实现拓扑到光滑的同痕，并应用于证明维度4中某些圆盘和球面的“拓扑=光滑”结果，同时获得Dax不变量的拓扑版本。

On symplectic caps

An important class of contact 3--manifolds are those that arise as links of rational surface singularities with reduced fundamental cycle. We explicitly describe symplectic caps (concave fillings) of such contact 3--manifolds. As an application, we present a new obstruction for such singularities to admit rational homology disk smoothings.

复截面的配边阻碍

Cobordism Obstructions to Complex Sections

本文将向量场配边推广到近复流形，定义并计算了复截面配边群，用 Chern 类刻画了流形可配备 r 个线性无关复截面的阻碍，并证明该阻碍在复配边环的某些乘法生成元上消失。

CAT(0) metrics on contractible manifolds

We prove that an open manifold $M$ of dimension at least $5$ which admits a complete CAT(0) polyhedral metric is pseudo-collarable, its fundamental group at infinity is strongly perfectly semistable and has vanishing Chapman-Siebenmann obstruction $τ_{\infty}(M)$. Moreover, this implies that $M$ is topologically collapsible, when $n\geq 6$. Conversely, any finite dimensional collapsible polyhedron is PL homeomorphic to a CAT(0) cubical complex.

Integrability of Poisson brackets

We show that various notions of integrability for Poisson brackets are all equivalent, and we give the precise obstructions to integrating Poisson manifolds. We describe the integration as a symplectic quotient, in the spirit of the Poisson sigma-model of Cattaneo and Felder. For regular Poisson manifolds we express the obstructions in terms of variations of symplectic areas. As an application of these results, we show that a Poisson manifold admits a complete symplectic realization if, and only if, it is integrable. We discuss also the integration of submanifolds and Morita equivalence of Poi…

Chern 类对光滑等变刚性的障碍

Chern class obstructions to smooth equivariant rigidity

本文研究光滑等变刚性的障碍，通过分析 Atiyah-Singer 类为零的 G-向量丛，将 Schultz 的无穷多个等变光滑结构例子推广到更一般情形，并证明对无穷多个素数 p，固定点集第二有理上同调非零时存在无穷多个稳定 G-光滑化。