Polish Groups Learning Seminar

Speaker: Aareyan Manzoor, University of Waterloo

"Metrics on Polish groups"

We investigate various compatible metrics that a Polish group admits. By Birkhoff-Kakutani, every Polish group admits a compatible left-invariant metric, and by being a Polish space, there is also a compatible metric which is complete. We discuss the relationship between these metrics, and introduce the class of CLI Polish groups, those Polish groups which admit a single compatible metric which is both left invariant and complete. We will mostly follow Section 2.2 of Gao's IDST book.

MC5403