We construct infinite families of closed connected orientable 3-manifolds obtained from certain triangulated 3-cells by pairwise identifications of their boundary faces. Our combinatorial constructions extend and complete a particular polyhedral scheme which Kim and Kostrikin used in 1995 and 1997 to define a series of spaces denoted M_3(n). Then we determine geometric presentations of the fundamental groups, and prove that many of the constructed manifolds are n-fold (non-strongly) cyclic coverings of the 3-sphere branched over some specified pretzel links.
CYCLIC BRANCHED COVERINGS OF SOME PRETZEL LINKS / Cavicchioli, Alberto; Spaggiari, Fulvia. - In: PERIODICA MATHEMATICA HUNGARICA. - ISSN 0031-5303. - STAMPA. - 67:1(2013), pp. 1-14. [10.1007/s10998-013-2837-z]
CYCLIC BRANCHED COVERINGS OF SOME PRETZEL LINKS
CAVICCHIOLI, Alberto;SPAGGIARI, Fulvia
2013
Abstract
We construct infinite families of closed connected orientable 3-manifolds obtained from certain triangulated 3-cells by pairwise identifications of their boundary faces. Our combinatorial constructions extend and complete a particular polyhedral scheme which Kim and Kostrikin used in 1995 and 1997 to define a series of spaces denoted M_3(n). Then we determine geometric presentations of the fundamental groups, and prove that many of the constructed manifolds are n-fold (non-strongly) cyclic coverings of the 3-sphere branched over some specified pretzel links.
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