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3-manifold spine cyclic presentations with seldom seen Whitehead graphs
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- Journal:
- Canadian Mathematical Bulletin , First View
- Published online by Cambridge University Press:
- 04 April 2025, pp. 1-19
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We consider a family of cyclic presentations and show that, subject to certain conditions on the defining parameters, they are spines of closed 3-manifolds. These are new examples where the reduced Whitehead graphs are of the same type as those of the Fractional Fibonacci presentations; here the corresponding manifolds are often (but not always) hyperbolic. We also express a lens space construction in terms of a class of positive cyclic presentations that are spines of closed 3-manifolds. These presentations then furnish examples where the Whitehead graphs are of the same type as those of the positive cyclic presentations of type
$\mathfrak {Z}$, as considered by McDermott.
