不可定向三维流形群的共轭问题

容许连续可消二元运算的流形是可定向的

Manifolds admitting a continuous cancellative binary operation are orientable

证明了容许连续可消二元运算的拓扑流形（可能有边界）是可定向的。这意味着默比乌斯带不允许取消连续二元运算。这回答了第二作者在2010年提出的一个问题。

Mapping classes are almost determined by their finite quotient actions

Given any connected compact orientable surface, a pair of mapping classes are said to be procongruently conjugate if they induce a conjugate pair of outer automophisms on the profinite completion of the fundamental group of the surface. For example, this occurs if they induce conjugate outer automorphisms on every characteristic finite quotient of the fundamental group. In this paper, it is shown that every procongruent conjugacy class of mapping classes, as a subset of the surface mapping class group, is the disjoint union of at most finitely many conjugacy classes of mapping classes. For any…

The enumeration of coverings of closed orientable Euclidean manifolds $G_3$ and $G_5$

There are only 10 Euclidean forms, that is flat closed three dimensional manifolds: six are orientable and four are non-orientable. The aim of this paper is to describe all types of $n$-fold coverings over orientable Euclidean manifolds $\mathcal{G}_{3}$ and $\mathcal{G}_{5}$, and calculate the numbers of non-equivalent coverings of each type. We classify subgroups in the fundamental groups $π_1(\mathcal{G}_{3})$ and $π_1(\mathcal{G}_{5})$ up to isomorphism and calculate the numbers of conjugated classes of each type of subgroups for index $n$. The manifolds $\mathcal{G}_{3}$ and $\mathcal{G}_…

几何可定向3-流形群的交换性分类空间

The classifying space for commutativity of geometric orientable 3-manifold groups

本文研究无限离散群的万有过渡交换主丛全空间，证明闭可定向几何3-流形基本群的该空间总是同伦等价于圆环楔和，并建立了相关同伦型结构结果。

具有Rokhlin性质的映射类群

Mapping class groups with the Rokhlin property

本研究分类了映射类群含稠密共轭类的连通可定向二维流形，并证明这类流形的映射类群含贫集共轭类等价于其映射类群平凡，推进了映射类群动力学性质研究。

Classifying spaces for the family of virtually abelian subgroups of orientable $3$-manifold groups

For a group $G$, let $\mathcal{F}_{n}$ be the family of all the subgroups of $G$ containing a subgroup isomorphic to $\mathbb{Z}^{r}$ for some $r=0,1,2,\dots ,n$ of finite index. Joecken, Lafont and Sánchez Saldaña computed the $\mathcal{F}_1$-dimension of 3-manifold groups. The goal of this article is to compute the $\mathcal{F}_n$-geometric dimension of 3-manifold groups for all $n\geq 2$.

双曲3-流形群是子群共轭可分的

Hyperbolic 3-Manifolds Groups are Subgroup Conjugacy Separable

一个群$G$称为子群共轭可分的，如果对于$G$的每对非共轭生成子群，存在$G$的有限商，其中这些子群的象不共轭.证明了双曲3-流形（闭流形或尖点流形）的基本群是子群共轭可分的。

A hyperbolic counterpart to Rokhlin's cobordism theorem

The purpose of the present paper is to prove existence of super-exponentially many compact orientable hyperbolic arithmetic $n$-manifolds that are geometric boundaries of compact orientable hyperbolic $(n+1)$-manifolds, for any $n \geq 2$, thereby establishing that these classes of manifolds have the same growth rate with respect to volume as all compact orientable hyperbolic arithmetic $n$-manifolds. An analogous result holds for non-compact orientable hyperbolic arithmetic $n$-manifolds of finite volume that are geometric boundaries, for $n \geq 2$.

关于3-流形的基本群嵌入其纽结群的问题

On embedding the fundamental group of a 3-manifold in one of its knot groups

本文给出了紧致连通可定向3-流形M含有纽结K的充要条件，使得M-K不可约且pi_1（M）嵌入pi_1（M-K）.这个结果提供了反例的猜想Lopes和Morales和特征，这些定向3流形，它是真的。

Twisted conjugacy in fundamental groups of geometric $3$-manifolds

A group $G$ has property $R_\infty$ if for every $ϕ\in Aut(G)$, there are an infinite number of $ϕ$-twisted conjugacy classes of elements in $G$. In this note, we determine the $R_\infty$-property for $G=π_1(M)$ for all geometric $3$-manifolds $M$.

双曲 $3$-流形群中的共轭区分陪集

Conjugacy Distinguished Cosets in Hyperbolic $3$-Manifold Groups

证明有限体积双曲3-流形群中，任何abelian子群的陪集是共轭区分的，并将此结果推广到loxodromic子群陪集与极大抛物子群类的共轭区分性。

Kaehler三流形群

Kaehlerian three-manifold groups

我们证明了，如果基本群的任意三个流形-不一定封闭，也不定向-是Kaehler群，那么它要么是有限的或基本群的封闭可定向曲面。

由曲面确定双曲三维流形

Determining hyperbolic 3-manifolds by their surfaces

本文证明了闭的可定向双曲三维流形的可分解类是由其基本群的曲面子群决定的。此外，我们还证明了，只有1000个闭的、可定向的、双曲3-流形具有相同的曲面集。

素三维流形的微分同胚群

Diffeomorphism groups of prime 3-manifolds

本文证明了基于Thurston几何$\text{Nil}$的紧致可定向非Haken三维流形的微分同胚群可形变收缩至等距群，从而完成了任意紧致可定向素三维流形微分同胚群同伦类型的确定。

三维变量和算子基本组

Groupes fondamentaux des varietes de dimension 3 et algebres d'operateurs

本文给出了3维流形的一个几何特征，它的基本群除1外的共轭类都是无限的，即von Neumann代数是$II_1$型因子：它们本质上是具有无限个基本群的3维流形，在这些基本群上不存在任何Seifert纤维化.换句话说，更精确地说，设$M$是一个紧连通3-流形，$Γ$是它的基本群，假设是无限的，并且除了1之外至少有一个有限共轭类。如果$M$是可定向的，那么$Γ$是塞弗特流形的基本群;如果$M$是不可定向的，那么$Γ$是塞弗特流形模$\Bbb P$在Heil和Whitten \cite{HeWh--94}意义下的基本群。我们大量使用的结果3流形，以及经典的结果（可以发现在书籍的亨佩尔，雅科，和沙伦），作为最近的（解决方案的塞弗特空间猜想）。