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The Geometry of the Handlebody Groups II: Dehn functions

Published 30 Apr 2018 in math.GR, math.GT, and math.MG | (1804.11133v1)

Abstract: We show that the Dehn function of the handlebody group is exponential in any genus $g\geq 3$. On the other hand, we show that the handlebody group of genus $2$ is cubical, biautomatic, and therefore has a quadratic Dehn function.

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