Hydra groups

Details Hydra groups Hydra groups

2010-02-09

arxiv.org/abs/1002.1945v2

Mathematics

Group Theory

26 pages, 3 figures

Scientific paper

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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