The geometry of one-relator groups satisfying a polynomial isoperimetric inequality
For every pair of positive integers p > q we construct a one-relator group R p,q whose Dehn function is ≃ n 2α where α = log 2 (2p/q). The group R p,q has no subgroup isomorphic to a Baumslag–Solitar group BS(m, n) with m ≠ ±n, but...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
| Published: |
American Mathematical Society
2018
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| Summary: | For every pair of positive integers p > q we construct a one-relator group R p,q whose Dehn function is ≃ n 2α where α = log 2 (2p/q). The group R p,q has no subgroup isomorphic to a Baumslag–Solitar group BS(m, n) with m ≠ ±n, but it 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. |
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