The algebraic structure of hyperbolic graph braid groups
Fuente:
arXiv
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| Autores principales: | , , , , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
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| _version_ | 1866911806705893376 |
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| author | Appiah, B. Dani, P. Ge, W. Hudson, C. Jain, S. Lemoine, M. Murphy, J. Murray, J. Pandikkadan, A. Schreve, K. Vo, H. |
| author_facet | Appiah, B. Dani, P. Ge, W. Hudson, C. Jain, S. Lemoine, M. Murphy, J. Murray, J. Pandikkadan, A. Schreve, K. Vo, H. |
| contents | Genevois recently classified which graph braid groups on $\ge 3$ strands are word hyperbolic. In the $3$-strand case, he asked whether all such word hyperbolic groups are actually free; this reduced to checking two infinite classes of graphs: sun and pulsar graphs. We prove that $3$-strand braid groups of sun graphs are free. On the other hand, it was known to experts that $3$-strand braid groups of most pulsar graphs contain surface subgroups. We provide a simple proof of this and prove an additional structure theorem for these groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08623 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The algebraic structure of hyperbolic graph braid groups Appiah, B. Dani, P. Ge, W. Hudson, C. Jain, S. Lemoine, M. Murphy, J. Murray, J. Pandikkadan, A. Schreve, K. Vo, H. Group Theory Geometric Topology Genevois recently classified which graph braid groups on $\ge 3$ strands are word hyperbolic. In the $3$-strand case, he asked whether all such word hyperbolic groups are actually free; this reduced to checking two infinite classes of graphs: sun and pulsar graphs. We prove that $3$-strand braid groups of sun graphs are free. On the other hand, it was known to experts that $3$-strand braid groups of most pulsar graphs contain surface subgroups. We provide a simple proof of this and prove an additional structure theorem for these groups. |
| title | The algebraic structure of hyperbolic graph braid groups |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2403.08623 |