The Geometry of the Handlebody Groups II: Dehn functions
classification
🧮 math.GR
math.GTmath.MG
keywords
dehnhandlebodyfunctiongenusgroupbiautomaticcubicalexponential
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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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