幂零群的Bockstein定理

Bockstein basis and resolution theorems in extension theory

We prove a generalization of the Edwards-Walsh Resolution Theorem: Theorem: Let G be an abelian group for which $P_G$ equals the set of all primes $\mathbb{P}$, where $P_G=\{p \in \mathbb{P}: \Z_{(p)}\in$ Bockstein Basis $ σ(G)\}$. Let n in N and let K be a connected CW-complex with $π_n(K)\cong G$, $π_k(K)\cong 0$ for $0\leq k< n$. Then for every compact metrizable space X with $XτK$ (i.e., with $K$ an absolute extensor for $X$), there exists a compact metrizable space Z and a surjective map $π: Z \to X$ such that (a) $π$ is cell-like, (b) $\dim Z \leq n$, and (c) $ZτK$.

关于具有 nilpotent 基本群的随机覆盖连通分支的中心极限定理

A central limit theorem for connected components of random coverings of manifolds with nilpotent fundamental groups

本文研究了当基本群为 nilpotent 时随机覆盖连通分支数量的中心极限定理，结合 du Sautoy 和 Grunewald 的子群增长 zeta 函数理论及 Delange 的 Wiener-Ikehara 定理推广。

扩张理论中的Hurewicz-Serre定理

Hurewicz-Serre Theorem in extension theory

本文致力于推广Cencelj-Dranishnikov定理的扩张性质的幂零CW复形的同调群。以下是本文的主要结果：\par { \bf定理}。假设$L$是一个幂零CW复形，$F$是$L$的包含$i$到其无限对称积$SP(L)$中的同伦纤维。如果$X$是可度量化空间，使得对于所有$k\ge 1$为$XτK(H_k(L),k)$，则对于所有$k\ge 2$为$XτK(π_k(F),k)$和$XτK(π_k(L),k)$。\par { \bf定理}。设$X$是一个可度量化的空间，使得$\dim(X) < \infty$或$X\in ANR$。设$L$是一个幂零CW复形，$SP(L)$是它的无限对称积.如果为$XτSP(L)$，则在以下情况下为$XτL$：\begin{itemize} \item[a.] $H_1(L)$ is finitely generated. \item[b.] $H_1(L)$ is a torsion group. \end{itemize}

幂零群幂零群的标度关系子与Dehn函数

Scaled relators and Dehn functions for nilpotent groups

一个齐次幂零李群有一个标度自同构，它由它的李代数的分次决定。许多证明的上界的德恩函数的这样一个群体取决于能够填补曲线与光盘兼容的这一分级;这种光盘的面积变化可预见的缩放自同构。在本文中，我们提出了寻找此类界限的组合方法。利用这种方法，我们给出了关于幂零群的Dehn函数的一些结果的新证明，证明了关于幂零群的中心幂和某些幂零的定理，并构造了第一个具有二次Dehn函数的无挠幂零群的例子.

A coarse embedding theorem for homological filling functions

We demonstrate under appropriate finiteness conditions that a coarse embedding induces an inequality of homological Dehn functions. Applications of the main results include a characterization of what finitely presentable groups may admit a coarse embedding into a hyperbolic group of geometric dimension $2$, characterizations of finitely presentable subgroups of groups with quadratic Dehn function with geometric dimension $2$, and to coarse embeddings of nilpotent groups into other nilpotent groups of the same growth and into hyperbolic groups.

幂零群与映射类群的子曲面子群的同余子群性质

Congruence Subgroup Property for nilpotent groups and subsurface subgroups of Mapping Class Groups

本文证明有限型曲面映射类群中两类子群满足同余子群性质，并顺带给出 Ben-Ezra–Lubotzky 定理的初等证明。