局部可指示群的凝聚性与单关系子积

On the classifying space for proper actions of groups with cyclic torsion

In this paper we introduce a common framework for describing the topological part of the Baum-Connes conjecture for a wide class of groups. We compute the Bredon homology for groups with aspherical presentation, one-relator quotients of products of locally indicable groups, extensions of $\mathbb{Z}^n$ by cyclic groups, and fuchsian groups. We take advantage of the torsion structure of these groups to use appropriate models of the universal space for proper actions which allow us, in turn, to extend some technology defined by Mislin in the case of one-relator groups.

关于单关系群及其群代数的凝聚性

On the coherence of one-relator groups and their group algebras

本文证明了单关系群的凝聚性，解决了 Gilbert Baumslag 的著名问题，并将该策略应用于上同调维数为2的群类，证明了二维复形基本群、交错展示群、部分 Coxeter 群及其群代数的凝聚性。

群对、相干性与 $K_0$ 的 Farrell--Jones 猜想

Group pairs, coherence and Farrell--Jones Conjecture for $K_0$

本文研究群对及其稳定子，证明局部可指标群的挠自由单关系乘积在因子相干时相干，并推广到群代数、扩张及 Farrell--Jones 猜想。

Coherence, local quasiconvexity, and the perimeter of 2-complexes

A group is coherent if all its finitely generated subgroups are finitely presented. In this article we provide a criterion for positively determining the coherence of a group. This criterion is based upon the notion of the perimeter of a map between two finite 2-complexes which is introduced here. In the groups to which this theory applies, a presentation for a finitely generated subgroup can be computed in quadratic time relative to the sum of the lengths of the generators. For many of these groups we can show in addition that they are locally quasiconvex. As an application of these results w…

$\ell^2$ Betti numbers and coherence of random groups

We study $\ell^2$ Betti numbers, coherence, and virtual fibring of random groups in the few-relator model. In particular, random groups with negative Euler characteristic are coherent, have $\ell^2$ homology concentrated in dimension 1, and embed in a virtually free-by-cyclic group with high probability. Similar results are shown with positive probability in the zero Euler characteristic case.

Coherence, subgroup separability, and metacyclic structures for a class of cyclically presented groups

We study a class $\mathfrak{M}$ of cyclically presented groups that includes both finite and infinite groups and is defined by a certain combinatorial condition on the defining relations. This class includes many finite metacyclic generalized Fibonacci groups that have been previously identified in the literature. By analysing their shift extensions we show that the groups in the class $\mathfrak{M}$ are are coherent, subgroup separable, satisfy the Tits alternative, possess finite index subgroups of geometric dimension at most two, and that their finite subgroups are all metacyclic. Many of t…