Schwartz's complex hyperbolic surface
Topics on hyperbolic geometry
Date: from June 20 to July 20
Venue: Lecture Hall, Institute for Advanced Study in Mathematics, No.7 teaching building
[ IASM visitors plan to organize an irregular seminar from June 20 to July 20. We will arrange about eight 1.5-hour introductory talks, on recent topics in hyperbolic geometry (and low-dimensional topology). The purpose of this seminar is to enhance communication and learn advances in the area. ]
Upcoming Seminar：
Date: | June 28 Mon.3:00pm -- 4:30 pm |
Speaker: | Jiming Ma( Fudan University) |
Title: | Schwartz's complex hyperbolic surface |
Abstract: | Let $G(4, 7)$ be a certain finitely presented group, in a celebrated paper of Schwartz in 2003, R. Schwartz considered a representation of $G(4, 7)$ into the isometry group of the complex hyperbolic plane. R. Schwartz determined the 3-manifold at infinity of the quotient complex hyperbolic surface via a sophisticated method. More precisely, the 3-manifold at infinity is a closed hyperbolic 3-orbifold with underlying space the 3-sphere and whose singularity locus is a two-components link equipped with a $\mathbb{Z}_2$-cone structure. In this talk, we will show the representation above is faithful, and determine the 4-dimensional topology of the complex hyperbolic surface via the handle structure. |
Full information about the Seminar can be seen at: http://www.iasm.zju.edu.cn/iasm/2021/0622/c58777a2397709/page.htm