不存在局部有限环面分解的单端3维流形

Local torus actions modeled on the standard representation

We introduce the notion of a local torus action modeled on the standard representation (for simplicity, we call it a local torus action). It is a generalization of a locally standard torus action and also an underlying structure of a locally toric Lagrangian fibration. For a local torus action, we define two invariants called a characteristic pair and an Euler class of the orbit map, and prove that local torus actions are classified topologically by them. As a corollary, we obtain a topological classification of locally standard torus actions, which is a generalization of the topological class…

Toric structures on near-symplectic 4-manifolds

A near-symplectic structure on a 4-manifold is a closed 2-form that is symplectic away from the 1-dimensional submanifold along which it vanishes and that satisfies a certain transversality condition along this vanishing locus. We investigate near-symplectic 4-manifolds equipped with singular Lagrangian torus fibrations which are locally induced by effective Hamiltonian torus actions. We show how such a structure is completely characterized by a singular integral affine structure on the base of the fibration whenever the vanishing locus is nonempty. The base equipped with this geometric struct…

四重极结构与局部四元数 торic 动作的兼容性

Tetraplectic structures compatible with local quaternionic toric actions

本文引入了四元数的 toric 几何类比，通过发展局部 $Q^n := Sp(1)^n$-作用理论，研究四元数 torus 作用的分类与特征对和欧拉类等不变量。

局部标准 T-伪流形的分类 over 伪流形的拓扑分层

Classification of locally standard $T$-pseudomanifolds over topological stratified pseudomanifolds

本文研究局部标准 T-伪流形的分类问题，证明满足特定条件的伪流形上的局部标准 T-伪流形可通过特征数据分类，扩展了 Davis-Januszkiewicz 对拟 toric 流形的分类结果。

Coxeter群Morse边界的连通性

Connectivity of Coxeter group Morse boundaries

本文研究Coxeter群Morse边界的连通性，通过定义图上的wide-avoidant等条件，刻画一般及直角Coxeter群边界连通与否，并给出无仿射情形下Morse测地射线的陪集停留特征。

相对双曲群边界的局部连通性

Local connectedness of boundaries for relatively hyperbolic groups

本文证明了相对单端的相对双曲群对的 Bowditch 边界具有局部连通性，去除了 Bowditch 先前结果中对外围子群的有限展示、端数及挠子群等全部额外限制。