3-manifold spine cyclic presentations with seldom seen Whitehead graphs

Gerald Williams

doi:10.4153/s0008439525000396

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arXiv · 2408.17125

3-manifold spine cyclic presentations with seldom seen Whitehead graphs

Gerald Williams

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Abstract

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.

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Gerald Williams. 2024-08-30. 3-manifold spine cyclic presentations with seldom seen Whitehead graphs. https://doi.org/10.4153/s0008439525000396

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