The geometry of one-relator groups satisfying a polynomial isoperimetric inequality
| Autor: | Gardam, Giles, Woodhouse, Daniel J. |
|---|---|
| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Proc. Amer. Math. Soc. 147 (2019) 125-129 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1090/proc/14238 |
| Popis: | For every pair of positive integers $p > q$ we construct a one-relator group $R_{p,q}$ whose Dehn function is $\simeq n^{2 \alpha}$ where $\alpha = \log_2(2p / q)$. The group $R_{p,q}$ has no subgroup isomorphic to a Baumslag-Solitar group $BS(m,n)$ with $m \neq \pm n$, but is not automatic, not CAT(0), and cannot act freely on a CAT(0) cube complex. This answers a long-standing question on the automaticity of one-relator groups and gives counterexamples to a conjecture of Wise. Comment: 6 pages, 1 figure; v3 final version to appear in Proceedings of the American Mathematical Society; v2 correct remark about residual finiteness |
| Databáze: | arXiv |
| Externí odkaz: |
|