循环群I和II的线性表示的拓扑等价性

纳米短语循环等价类的有限型不变量

Finite type invariants for cyclic equivalence classes of nanophrases

在本文中，我们定义了纳米短语循环等价类的有限型不变量，并构造了泛不变量。此外，我们确定了普遍的有限型不变量的程度1本质上与连接矩阵。众所周知，Arnold的基本不变式扩展到有符号的话是有限型不变量的程度2，由Fujiwara。我们给出了这个结果的另一个证明，并表明这些不变量不提供2度的泛不变量。

Assembly maps for topological cyclic homology of group algebras

We use assembly maps to study $\mathbf{TC}(\mathbb{A}[G];p)$, the topological cyclic homology at a prime $p$ of the group algebra of a discrete group $G$ with coefficients in a connective ring spectrum $\mathbb{A}$. For any finite group, we prove that the assembly map for the family of cyclic subgroups is an isomorphism on homotopy groups. For infinite groups, we establish pro-isomorphism, (split) injectivity, and rational injectivity results, as well as counterexamples to injectivity and surjectivity. In particular, for hyperbolic groups and for virtually finitely generated abelian groups, we…

On topological classification of finite cyclic actions on bordered surfaces

In [Tohoku Math. J. 62 (2010), 45--53] the second author showed that, except for a few cases, the order $N$ of a cyclic group of self-homeomorphisms of a closed orientable topological surface $S_g$ of genus $g \geq 2$ determines the group up to a topological conjugation, provided that $N\geq 3g$. The first author et al. undertook in [Collect. Math. 67 (2016), 415--429] a more general problem of topological classification of such group actions for $N>2(g-1)$. In [Rev. R. Acad. Cienc. Exactas Fis. Nat., Ser. A. Mat. (RACSAM) 110 (2016), 303--320] we considered the analogous problem for closed no…

某些非定向四维流形的拓扑分类（其基本群阶为2 mod 4）

Topological classification of certain nonorientable 4-manifolds with cyclic fundamental group of order 2 mod 4

本文通过剪切和粘贴构造，利用经典和修改后的手术理论结果，对基本群阶为2p的非定向四维流形进行拓扑分类，并提出若干问题以完善分类。

循环泡沫拓扑域论

Cyclic Foam Topological Field Theories

本文提出了循环泡沫拓扑域论的一个公理。这就是拓扑域论，对应于弦论，其中粒子是任意的图形。在这种情况下，世界表面是具有一维奇点的二维流形。证明了循环泡沫拓扑域论与图-Cardy-Frobenius代数一一对应，即$(A,B_\star,ϕ)$族，其中$A=\{A^s|s\in S\}$是交换结合Frobenius代数族，$B_\star = \bigoplus_{σ\inΣ} B_σ$是Frobenius型图结合代数，$ϕ=\{ϕ_σ^s: A^s\to (B_σ)|s\in S,σ\in Σ\}$是特殊表示族.给出了循环泡沫拓扑域论及其图的构造实例--Cardy-Frobenius代数

拓扑量子场论与强位移等价

Topological Quantum Field Theory And Strong Shift Equivalence

给定一个d+1维的TQFT和一个闭（d+1）维流形M的无限循环覆盖，我们定义了一个取值于矩阵的强移位等价类的不变量.强移位等价的概念起源于R。威廉姆斯在符号动力学方面的工作。与TQFT和无限循环覆盖相关联的Turaev-Viro模则由该矩阵远离零的Jordan形式给出。如果M的边界有一个圆因子，并且边界的无限循环覆盖是标准的，则也定义了这个不变量。我们定义了一个变体的TQFT相关的有限群G已研究奎因。通过这种方式，我们恢复了由于D的链接不变量。Silver和S.威廉姆斯我们还获得了一个变化的Silver-Williams不变量，通过使用TQFT与G在其未修改的形式。