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Abstract: We first discuss various embedding results for groups in the literature. Then we talk about how could one embed a group of type F_n into a group of type F_n with no proper finite index subgroup quasi-isometrically. The embedding we have uses the so called labelled Thompson groups, and it is functorial. We also show that the labeled Thompson group is always bounded acyclic. As a corollary, one could embed any group of type F_n into a bounded acyclic group of type F_n quasi-isometrically. This is based on a joint work with Fan Wu, Mengfei Zhao and Zixiang Zhou.
Bio: Dr. Xiaolei Wu is an Young Investator at the Shanghai Center for Mathematical Sciences, Fudan University. He obtained his Ph.D in SUNY Binghamton working with F. Thomas Farrell. He was a postdoc at Free University of Berlin, MPI Bonn, Univeristy of Bonn and Bielefeld University. He joined Fudan in 2021. His research interests includes Geometric group theory, manifold topology and Algebraic K-theory.
