Nearly-linear solution to the word problem for 3-manifold groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909991110180864 |
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| author | Sisto, Alessandro Zbinden, Stefanie |
| author_facet | Sisto, Alessandro Zbinden, Stefanie |
| contents | We show that the word problem for any 3-manifold group is solvable in time $O(n\log^3 n)$. Our main contribution is the proof that the word problem for admissible graphs of groups, in the sense of Croke and Kleiner, is solvable in $O(n\log n)$; this covers fundamental groups of non-geometric graph manifolds. Similar methods also give that the word problem for free products can be solved ``almost as quickly'' as the word problem in the factors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18029 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nearly-linear solution to the word problem for 3-manifold groups Sisto, Alessandro Zbinden, Stefanie Group Theory Geometric Topology We show that the word problem for any 3-manifold group is solvable in time $O(n\log^3 n)$. Our main contribution is the proof that the word problem for admissible graphs of groups, in the sense of Croke and Kleiner, is solvable in $O(n\log n)$; this covers fundamental groups of non-geometric graph manifolds. Similar methods also give that the word problem for free products can be solved ``almost as quickly'' as the word problem in the factors. |
| title | Nearly-linear solution to the word problem for 3-manifold groups |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2407.18029 |