(Un)distorted stabilisers in the handlebody group

Sebastian Hensel (Munich)

Monday 3rd June 16:00-17:00 Maths 311B

Abstract

We will discuss features of the word geometry of the mapping class group of a 3-dimensional
handlebody that set it apart from the case of surface mapping class groups. In particular, in the mapping class group of a surface, stabilisers of curves are quasi-isometrically embedded for all curves. Handlebody groups show a different behaviour (analogous to the situation in the group of outer automorphisms of the free group): stabilisers of meridians are quasi-isometrically embedded, while stabilisers of other curves may be exponentially distorted.

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