Georgia Institute of Technology College of Sciences

The fine curve graph of a surface S was introduced by Bowden–Hensel–Webb in 2019 to study the diffeomorphism group of S. We consider a variant of this graph, called the fine 1-curve graph, whose vertices are essential simple closed curves and edges connect curves that intersect in at most one point. Building on the works of Long–Margalit–Pham–Verberne–Yao and Le Roux–Wolff, we show that the automorphism group of the fine 1-curve graph is isomorphic to the homeomorphism group of S. This is joint work with Katherine W. Booth and Daniel Minahan.