Virtual Seminar on

Geometry and Topology

https://visgat.cayley.kr

How to join

Zoom Link http://cayley.kr/vz

Time Wed 4 pm or Thursday 9 am (or so) in KST (Korea Standard Time)

2022

October 12 (W) and 14 (F), 10 am

In-person KIAS 1503

Online http://cayley.kr/vz

Gromov boundary extended

Gromov boundary provides a useful compactification for all infinite-diameter Gromov hyperbolic spaces. It consists of all geodesic rays starting at a given base-point and it has been an essential tool in the study of the coarse geometry of hyperbolic groups. In this study we introduce two topological spaces that are natural analogs of the Gromov boundary for a larger class of metric spaces. First we construct the sublinearly Morse boundaries and show that it is a QI-invariant topological space that can be associated to all finitely generated groups. Furthermore, for many groups, the sublinear boundary can be identified with the Poisson boundaries of the associated group, thus providing a QI-invariant model for Poisson boundaries. This result answers the open problems regarding QI-invariant models of CAT(0) groups and the mapping class group. Lastly, for a subset of the metric spaces we define a compactification of the sublinearly Morse boundary and show that in these cases they are naturally identified with the Bowditch boundary. This is a series of joint work with Kasra Rafi and Giulio Tiozzo.



Organizers

Harry Hyungryul Baik (KAIST)

Sam Sang-hyun Kim (KIAS)

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