Journal of Lie Theory

no. 4
A Generalization of Helling-Kim-Mennicke Groups and Manifolds
Journal of Lie Theory, Volume 17 (2007) no. 4, pp. 857-867
We construct an infinite family of closed connected orientable 3-manifolds by pairwise identifications of faces in the boundary of certain polyhedral 3-cells. We determine geometric presentations (that is, induced by Heegaard diagrams of the constructed manifolds) of the fundamental group, and study the split extension of it. Then we prove that these manifolds are n-fold cyclic coverings of the 3-sphere branched over some pretzel links. Our results generalize those of Helling, Kim and Mennicke [Comm. in Algebra 23 (1995) 5169--5206] and Cavicchioli and Paoluzzi [Manuscripta Math. 101 (2000) 457--494] on cyclic branched coverings of the Whitehead link, and their fundamental groups.
DOI: 10.5802/jolt.475
Classification: 57M12, 57M25, 53C30, 20F05, 20F34, 57M50, 57N10
Keywords: 3-manifolds, group presentations, spines, orbifolds, polyhedral schemata, branched coverings, hyperbolic structure 
@article{JOLT_2007_17_4_a6,
     author = {E. Barbieri and A. Cavicchioli and F. Spaggiari},
     title = {A {Generalization} of {Helling-Kim-Mennicke} {Groups} and {Manifolds}},
     journal = {Journal of Lie Theory},
     pages = {857--867},
     year = {2007},
     volume = {17},
     number = {4},
     doi = {10.5802/jolt.475},
     zbl = {1171.57002},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.475/}
}
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E. Barbieri; A. Cavicchioli; F. Spaggiari. A Generalization of Helling-Kim-Mennicke Groups and Manifolds. Journal of Lie Theory, Volume 17 (2007) no. 4, pp. 857-867. doi: 10.5802/jolt.475

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