7 papers
-manifold groups are linear
Xiaolei Wu, Shengkui Ye
We prove that the fundamental group of every compact graph -manifold is linear over the complex numbers. As a corollary, all fundamental groups of compact -manifolds are line…
Pure braid groups are RFRS
Xiaolei Wu, Shengkui Ye
Agol in his 2014 ICM proceedings article \cite[Question 11]{Agol14} asks whether braid groups are (virtually) RFRS. We answer this positively by showing that pure braid groups are…
Abstract twisted Brin--Thompson groups
Francesco Fournier-Facio, Xiaolei Wu, Matthew C. B. Zaremsky
Given a group acting faithfully on a set , one gets a simple group denoted , called a twisted Brin--Thompson group. In this paper we drop the faithfulness assumption,…
Ample groupoids that are neither almost finite nor purely infinite
Xiaolei Wu, Mengfei Zhao, Xin Ma
We study a question of Matui and varations of it on minimal ample groupoids that are neither almost finite nor purely infinite. We first observe that there are already effective mi…
Embedding groups into acyclic groups
Martin Palmer, Xiaolei Wu
We show that labelled Thompson groups and twisted Brin--Thompson groups are all acyclic. This allows us to prove several new embedding results for groups. First, every group of typ…
Some questions related to free-by-cyclic groups and tubular groups
Xiaolei Wu, Shengkui Ye
We prove that a CAT(0) free-by-cyclic tubular group with a single vertex is virtually special, but many of them cannot virtually act freely and cocompactly on CAT(0) cube complexes…
Embedding groups into boundedly acyclic groups
Fan Wu, Xiaolei Wu, Mengfei Zhao +1
We show that the \sϕ-labeled Thompson groups and the twisted Brin--Thompson groups are boundedly acyclic. This allows us to prove several new embedding results for groups. First, e…