The model theory of the curve graph

Abstract: The curve graph of a surface of finite type is a graph that encodes the combinatorics of isotopy classes of simple closed curves. It is a fundamental tool for the study of the geometric group theory of the mapping class group. In 1987 N.K. Ivanov proved that the automorphism group of the curve graph is the extended mapping class group. In the following decades, many people proved analogous results for many "similar" graphs, such as the pants graph, the arc graph, and so on. In response to these results, N.V. Ivanov formulated a meta-conjecture which asserts that any "natural and sufficiently rich" object associated to a surface has automorphism group isomorphic to the extended mapping class group.

We provide a model theoretical framework for Ivanov’s meta-conjecture and conduct a thorough study of curve graphs from the model theoretic point of view, with particular emphasis in the problem of interpretability between different "similar" geometric complexes. In particular, we prove that the curve graph of a surface of finite type is w-stable. This talk does not assume any prior knowledge in model theory.

This is joint work with Thomas Koberda (Virginia) and Javier de la Nuez Gonzalez (KIAS).

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( paper | slides )

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Geometry and topology online

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The talks start at 13:30. Talks are typically fifty minutes long, with ten minutes for questions.

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