Groups and Dynamics Seminar

In this talk, I will describe a measurable analog of Euler’s formula for bounded-degree Borel planar graphs. Given a pmp graph, one obtains a relation between the measure of the vertex set, the cost, and face cost, generalizing the classical Euler formula. This measurable Euler characteristic interacts naturally with cost and amenability/hyperfiniteness, and, in ongoing work, gives new bounds on measurable chromatic number.