Surveys in Differential Geometry

Volume 25 (2020)

Toward and after virtual specialization in $3$-manifold topology

Pages: 215 – 252



Yi Liu (Beijing International Center for Mathematical Research, Peking University, Beijing, China)

Hongbin Sun (Department of Mathematics, Rutgers University, Piscataway, New Jersey, U.S.A.)


This article surveys works in $3$‑manifold topology after the proof of the virtual Haken conjecture. It reviews the virtual specialization of $3$‑manifold groups, and some following development of methods, and applications in recent years.

The first author is partially supported by the Recruitment Program of Global Youth Experts of China and the Qiushi Outstanding Young Scholar Reward. The second author is partially supported by NSF Grant No. DMS-1840696 of the United States.

Published 13 July 2022