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 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.
A generalization of Helling-Kim-Mennicke groups and manifolds / E., Barbieri; Cavicchioli, Alberto; Spaggiari, Fulvia. - In: JOURNAL OF LIE THEORY. - ISSN 0949-5932. - STAMPA. - 17:4(2007), pp. 857-867.
A generalization of Helling-Kim-Mennicke groups and manifolds
CAVICCHIOLI, Alberto;SPAGGIARI, Fulvia
2007
Abstract
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 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.
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