We study the topology and geometry of some series of closed connected orientable 3-manifolds constructed as honey-comb spaces. These manifolds are quotients of certain polyhedral 3-cells by pairwise identification of their boundary faces. We determine geometric presentations of the fundamental group and study the split extension of it. Then we describe geometric structures, homeomorphism type and covering properties of our manifolds which are shown to be cyclic coverings of the 3-sphere branched over known links with two components. Finally, we answer open questions on certain manifolds, defined by Kim and Kostrikin, and give a complete classification of them.
SOME SERIES OF HONEY-COMB SPACES / E., Barbieri; Cavicchioli, Alberto; Spaggiari, Fulvia. - In: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS. - ISSN 0035-7596. - STAMPA. - 39:2(2009), pp. 381-398. [10.1216/RMJ-2009-39-2-381]
SOME SERIES OF HONEY-COMB SPACES
CAVICCHIOLI, Alberto;SPAGGIARI, Fulvia
2009
Abstract
We study the topology and geometry of some series of closed connected orientable 3-manifolds constructed as honey-comb spaces. These manifolds are quotients of certain polyhedral 3-cells by pairwise identification of their boundary faces. We determine geometric presentations of the fundamental group and study the split extension of it. Then we describe geometric structures, homeomorphism type and covering properties of our manifolds which are shown to be cyclic coverings of the 3-sphere branched over known links with two components. Finally, we answer open questions on certain manifolds, defined by Kim and Kostrikin, and give a complete classification of them.
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