Publication at Faculty of Mathematics and Physics |
2019
Abstract
We study automorphism groups of sparse graphs from the viewpoint of topological dynamics and the Kechris, Pestov, Todorcevic correspondence. We investigate amenable and extremely amenable subgroups of these groups using the space of orientations of the graph and results from structural Ramsey theory.
Resolving one of the open questions in the area, we show that Hrushovski's example of an omega-categorical sparse graph has no omega-categorical expansion with extremely amenable automorphism group.