- This event has passed.
Seminar: Mr. Cong He
August 18, 2020 @ 2:00 pm - 3:00 pm
Due to the COVID-19 Pandemic, the University has instruction to cancel all in-person events through the Summer semester to adhere to city and state orders limiting public gatherings. Events still running must now take place Online— listed events will include a link in which one may access the Online webspace:
To view Mr. He’s seminar, enter his Online chatroom via Microsoft Teams— it will open one hour prior to the event at 2:00 pm on Tuesday, August 18.
Hyperbolic groups with boundary a Sierpinski-Jakobsche space
Mr. Cong He
University of Wisconsin-Milwaukee
PhD Graduate Student – Teaching Assistant
“I will discuss some Hyperbolic groups with boundary a Sierpinski-Jakobsche space. Based on classical Riemannian geometry, one might expect the (visual) boundary of every closed aspherical manifold to be a sphere, and the boundary of every compact aspherical manifold with boundary to be a sphere or a Sierpinski space. As it turns out, these expectations are incorrect. Work by Davis, Januszkiewicz, Ancel and Guilbault showed that boundaries of Gromov hyperbolic and CAT(0) closed manifolds can be quite complicated. By analyzing that work more carefully, Fischer showed that those boundaries are frequently beautiful fractal objects known as Jakobsche spaces. More recently, Lafont and Tshishiku showed that there are aspherical manifolds with boundary whose corresponding group boundary is neither a sphere nor Sierpinski space. In this talk, I will discuss some Hyperbolic groups with boundary a Sierpinski-Jakobsche space which will be defined. More precisely, I will talk about the rough idea of the following: For each homology 3-sphere H^3, there existes an aspherical 4-manifold with boundary M^4 whose fundamental group is hyperbolic and the Gromov boundary of it is a Sierpinski-Jakobsche space.”