Connectivity of partial basis complexes of freely decomposable groups
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918147613786112 |
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| author | Brück, Benjamin Piterman, Kevin Ivan |
| author_facet | Brück, Benjamin Piterman, Kevin Ivan |
| contents | We show that the complex of partial bases of the free group of rank $n$, where vertices are seen up to conjugation, is Cohen--Macaulay of dimension $n-1$. This positively answers a conjecture raised by Day and Putman. We prove our results in the more general context of freely decomposable groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17121 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Connectivity of partial basis complexes of freely decomposable groups Brück, Benjamin Piterman, Kevin Ivan Geometric Topology Group Theory 20F65, 20E06, 57M07 We show that the complex of partial bases of the free group of rank $n$, where vertices are seen up to conjugation, is Cohen--Macaulay of dimension $n-1$. This positively answers a conjecture raised by Day and Putman. We prove our results in the more general context of freely decomposable groups. |
| title | Connectivity of partial basis complexes of freely decomposable groups |
| topic | Geometric Topology Group Theory 20F65, 20E06, 57M07 |
| url | https://arxiv.org/abs/2410.17121 |