Combinatorial isoperimetric inequality for the free factor complex
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913793549795328 |
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| author | Gupta, Radhika |
| author_facet | Gupta, Radhika |
| contents | We show that the free factor complex of the free group of rank greater than or equal to 4 does not satisfy a combinatorial isoperimetric inequality: that is, for every natural number N, there is a loop c_N of length 4 in the free factor complex such that the number of 2-simplices required to fill c_N grows at least as a linear function of N. To prove the result, we construct a coarsely Lipschitz function from the `upward link' of a free factor to the set of integers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_09973 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Combinatorial isoperimetric inequality for the free factor complex Gupta, Radhika Group Theory Geometric Topology 20F65, 57M60, 20E36 We show that the free factor complex of the free group of rank greater than or equal to 4 does not satisfy a combinatorial isoperimetric inequality: that is, for every natural number N, there is a loop c_N of length 4 in the free factor complex such that the number of 2-simplices required to fill c_N grows at least as a linear function of N. To prove the result, we construct a coarsely Lipschitz function from the `upward link' of a free factor to the set of integers. |
| title | Combinatorial isoperimetric inequality for the free factor complex |
| topic | Group Theory Geometric Topology 20F65, 57M60, 20E36 |
| url | https://arxiv.org/abs/2308.09973 |