Nearly-linear solution to the word problem for 3-manifold groups
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.18029
- arXiv:
- arXiv:2407.18029
- Bibcode:
- 2024arXiv240718029S
- Keywords:
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- Mathematics - Group Theory;
- Mathematics - Geometric Topology
- E-Print:
- 24 pages, 1 figure