Injective spaces, Helly graphs, and their automorphism groups

Abstract: Injective metric spaces are classical and important (injective) objects studied within metric geometry. Their combinatorial counterpart are Helly graphs. I will present basic facts in the two settings and show how they relate to each other. Then I will focus on groups acting by automorphisms on Helly graphs. Recently, it has been shown that many classical groups, including Gromov hyperbolic groups, Garside groups, CAT(0) cubical groups, and braid groups act "nicely" on Helly graphs. This allows one to obtain new results on these classical groups, using nonpositive-curvature-like behavior of Helly graphs.

computational geometrydiscrete mathematicscommutative algebracombinatorics

Audience: researchers in the topic

Copenhagen-Jerusalem Combinatorics Seminar

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