Abstract

In this talk, I will discuss progress on profinite properties of 3-manifold topology in recent years. A profinite property of a finitely generated group is a property that is determined by all of its finite quotient groups, and for 3-manifolds we refer to their fundamental groups. Roughly speaking, profinite completions of 3-manifold groups often determine the 3-manifold up to finitely many possibilities. To go from the finiteness to uniqueness is sometimes possible, but still open for the general case.

Profile

Yi Liu is a professor at Beijing International Center for Mathematical Research (BICMR) in Peking University. His research interest lies primarily in 3-manifold topology and hyperbolic geometry. He received his Ph.D. degree in 2012 in University of California at Berkeley. During 2012--2015, he was appointed at California Institute of Technology as a Taussky--Todd lecturer. He has joined BICMR since 2015.