Howie, J and Williams, G (2017) Fibonacci type presentations and 3-manifolds. Topology and its Applications, 215. pp. 24-34. DOI https://doi.org/10.1016/j.topol.2016.10.012
Howie, J and Williams, G (2017) Fibonacci type presentations and 3-manifolds. Topology and its Applications, 215. pp. 24-34. DOI https://doi.org/10.1016/j.topol.2016.10.012
Howie, J and Williams, G (2017) Fibonacci type presentations and 3-manifolds. Topology and its Applications, 215. pp. 24-34. DOI https://doi.org/10.1016/j.topol.2016.10.012
Abstract
We study the cyclic presentations with relators of the form xixi+mx?1 i+k and the groups they define. These ?groups of Fibonacci type? were intro- duced by Johnson and Mawdesley and they generalize the Fibonacci groups F(2, n) and the Sieradski groups S(2, n). With the exception of two groups, we classify when these groups are fundamental groups of 3-manifolds, and it turns out that only Fibonacci, Sieradski, and cyclic groups arise. Using this classification, we completely classify the presentations that are spines of 3-manifolds, answering a question of Cavicchioli, Hegenbarth, and Repov?s. When n is even the groups F(2, n), S(2, n) admit alternative cyclic presenta- tions on n/2 generators. We show that these alternative presentations also arise as spines of 3-manifolds.
Item Type: | Article |
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Additional Information: | 16 pages, 3 figures |
Uncontrolled Keywords: | Fibonacci group; Sieradski group; cyclically presented group; 3-manifold group; spine of a manifold |
Subjects: | Q Science > QA Mathematics |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 03 Nov 2016 12:00 |
Last Modified: | 07 Aug 2024 20:08 |
URI: | http://repository.essex.ac.uk/id/eprint/17878 |
Available files
Filename: HowieWilliams-FibonacciTypePresentations.pdf