Hydra groups
Will Dison and Tim Riley
Commentarii Mathematici Helvetici, 88(3), pages 507–540, 2013
We give examples of CAT(0), biautomatic, free–by–cyclic,
one–relator groups which have finite–rank free subgroups of
huge (Ackermannian) distortion. This leads to elementary examples of
groups whose Dehn functions are similarly extravagant. This behaviour
originates in manifestations of
Hercules–versus–the–hydra battles in
string–rewriting.
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