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Snowflake groups and conjugator length functions with non-integer exponents
Martin Bridson and Timothy Riley We prove that the snowflake groups $B_{pq}$, indexed by pairs of positive integers $p>q$, have conjugator length functions $\text{CL}(n)\simeq n$ and annular Dehn functions $\text{Ann}(n) \simeq n^{2\alpha}$, where $\alpha = \log_2(2p/q)$. Then, building on $B_{pq}$, we construct groups $\tilde{B}_{pq}^+$, for which $\text{CL}(n)\simeq n^{\alpha+1}$. Thus the conjugator length spectrum and the annular Dehn function spectrum are both dense in the range $[2,\infty)$. .
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