A characterization of alternating link exteriors in terms of cubed complexes

Combinatorial local convexity implies convexity in finite dimensional CAT(0) cubed complexes

We give a proof to the following theorem, which is well-known among experts: A connected subcomplex $W$ of a finite dimensional CAT(0) cubed complex $X$ is convex if and only if Lk$(v, W)$ is a full subcomplex of Lk$(v, X)$ for every vertex $v$ of $W$.

一个用于纽结外部本质曲面复形的图像 - 核 - 重构程序

Essential-Surface Complexes of Knot Exteriors: Image, Kernel, and Reconstruction

研究纽结外部保子午线映射类群对本质曲面不相交复形的作用，组织四个刚性问题，通过条件约化原则等方法，对环面纽结、双曲纽结等多种纽结外部情况进行分析，给出图像 - 核簿记和重构框架。

A-infinity structure on simplicial complexes

A discrete (finite-difference) analogue of differential forms is considered, defined on simplicial complexes, including triangulations of continuous manifolds. Various operations are explicitly defined on these forms, including exterior derivative and exterior product. The latter one is non-associative. Instead, as anticipated, it is a part of non-trivial A-infinity structure, involving a chain of poly-linear operations, constrained by nilpotency relation: (d + \wedge + m + ...)^n = 0 with n=2.

不可压缩Seifert曲面的复形的可缩性：Kakimizu问题的纽结情形

Exchange complexes and contractibility of the complex of incompressible Seifert surfaces

本文证明非平凡纽结的不可压缩Seifert曲面同痕类复形及其亏格截断均可缩，通过提出旗交换复形可缩的纯组合定理，绕过了先前投影良定义性的障碍，并推广至满足特定条件的链环情形。

有限元外微积分：从霍奇理论到数值稳定性

Finite element exterior calculus: from Hodge theory to numerical stability

本文融合数值分析与拓扑几何两个研究方向，通过抽象希尔伯特空间框架和有限元外微分形式，建立了霍奇拉普拉斯算子的稳定离散方法，并应用于弹性力学方程。