Gevrey series in quantum topology

关于数字拓扑学中不动点论断的评注（6）

Remarks on Fixed Point Assertions in Digital Topology, 6

本文是数字拓扑不动点论断评注系列的第六篇，继续探讨已发表数字度量空间不动点相关论断中的问题。

关于数字拓扑中不动点断言的评论，7

Remarks on Fixed Point Assertions in Digital Topology, 7

本文延续系列讨论，指出已发表的数字图像不动点断言中的缺陷。

关于数字拓扑中不动点断言的评述，8

Remarks on Fixed Point Assertions in Digital Topology, 8

该论文延续系列工作，继续审视既有数字图像不动点断言文献中的论证缺陷。

通过编织解码自缠结链电路拓扑中的手性

Decoding chirality in circuit topology of a self entangled chain through braiding

本研究将电路拓扑的结构建方法融入辫子理论框架，计算不同拓扑关系下软接触组合的Jones多项式并证明其因式分解特性，为分子结手性分析及手性缠结链设计提供工具，可应用于材料科学等领域。

From state integrals to q-series

It is well-known to the experts that multi-dimensional state integrals of products of Faddeev's quantum dilogarithm which arise in Quantum Topology can be written as finite sums of products of basic hypergeometric series in q=e^{2πiτ} and \tilde{q}=e^{-2πi/τ}. We illustrate this fact by giving a detailed proof for a family of one-dimensional integrals which includes state-integral invariants of 4_1 and 5_2 knots.

Long-time behavior of 3 dimensional Ricci flow -- C: 3-manifold topology and combinatorics of simplicial complexes in 3-manifolds

In the third part of this series of papers, we establish several topological results that will become important for studying the long-time behavior of Ricci flows with surgery. In the first part of this paper we recall some elementary observations in the topology of 3-manifolds. The main part is devoted to the construction of certain simplicial complexes in a given 3-manifold that exhibit useful intersection properties with embedded, incompressible solid tori. This paper is purely topological in nature and Ricci flows will not be used.