Curve graphs: exhaustions by rigid sets and the co-Hopfian property

Abstract: Since Ivanov's celebrated first result, many rigidity theorems for various variants of the curve graph of surfaces have been proven. Among these, there is a cluster of results regarding the existence of exhaustion via finite subgraphs which are rigid (that is such that every embedding is induced by an automorphism of the whole graph). From this property, interesting per se, the co-Hopfian property of the graphs immediately follows. In this talk I will present the classical results in the fields, as well as some new cases, which point toward conjecturing that most curve graphs on finite-type surfaces should admit exhaustions by rigid sets, in line with Ivanov's Metaconjecture.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and topology online

Series comments: You can also find up-to-date information on the seminar homepage - warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/geomtop/

The talks start five minutes after the hour. Talks are typically 55 minutes long, including time for questions.