Problems on handlebody groups
Abstract
We survey a number of constructions and open problems related to the handlebody group, with a focus on recent trends in geometric group theory, (co)homological properties, and its relationship to outer automorphism groups of free groups. We also briefly describe how the cheap α-rebuilding property of Abert, Bergeron, Fraczyk, and Gaboriau can be applied using the disc complex to deduce results about the homology growth of the handlebody group.
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