3-manifold spine cyclic presentations with seldom seen Whitehead graphs
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915226965770240 |
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| author | Williams, Gerald |
| author_facet | Williams, Gerald |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_17125 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 3-manifold spine cyclic presentations with seldom seen Whitehead graphs Williams, Gerald Geometric Topology Group Theory 20F05, 57M05, 57M50 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. |
| title | 3-manifold spine cyclic presentations with seldom seen Whitehead graphs |
| topic | Geometric Topology Group Theory 20F05, 57M05, 57M50 |
| url | https://arxiv.org/abs/2408.17125 |