2025/02/28 by Andrew, Naomi, Hensel, Sebastian, Hughes, Sam +1
#20E26 #20E36 #20F65 (Primary) 20E18 #20J05 #20J06 #57K20 #57M07 #57M99 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2502.21177
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.