Random Dehn function of groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915453416243200 |
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| author | García-Mejía, Jerónimo Goldsborough, Antoine |
| author_facet | García-Mejía, Jerónimo Goldsborough, Antoine |
| contents | In this note, we study the notion of random Dehn function and compute an asymptotic upper bound for finitely presented acylindrically hyperbolic groups whose Dehn function is at most polynomial. By showing that in these cases, if the group is not hyperbolic, then the random Dehn function is strictly smaller than the usual Dehn function we confirm Gromov's intuition albeit in a different model. In fact, we show that in these cases the random Dehn function is at most quadratic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12715 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Random Dehn function of groups García-Mejía, Jerónimo Goldsborough, Antoine Group Theory Metric Geometry Probability In this note, we study the notion of random Dehn function and compute an asymptotic upper bound for finitely presented acylindrically hyperbolic groups whose Dehn function is at most polynomial. By showing that in these cases, if the group is not hyperbolic, then the random Dehn function is strictly smaller than the usual Dehn function we confirm Gromov's intuition albeit in a different model. In fact, we show that in these cases the random Dehn function is at most quadratic. |
| title | Random Dehn function of groups |
| topic | Group Theory Metric Geometry Probability |
| url | https://arxiv.org/abs/2411.12715 |