We study some series of finite presentations of groups and fibered closed 3-manifolds obtained by side pairings of boundary faces on certain symmetric polyhedral 3-balls. These spaces cyclically extend some classical examples, and contain a family of manifolds constructed by Kim and Kostrikin in Sbornik Math. 188 (1997). Then we describe some covering properties of our manifolds, and show that many of them are hyperelliptic. Finally, we completely classify Kim-Kostrikin manifolds, and determine their Seifert invariants.
Seifert hyperelliptic manifolds / E., Barbieri; Cavicchioli, Alberto; Spaggiari, Fulvia. - In: INTERNATIONAL JOURNAL OF PURE AND APPLIED MATHEMATICS. - ISSN 1311-8080. - STAMPA. - 6:(2003), pp. 317-342.
Seifert hyperelliptic manifolds
CAVICCHIOLI, Alberto;SPAGGIARI, Fulvia
2003
Abstract
We study some series of finite presentations of groups and fibered closed 3-manifolds obtained by side pairings of boundary faces on certain symmetric polyhedral 3-balls. These spaces cyclically extend some classical examples, and contain a family of manifolds constructed by Kim and Kostrikin in Sbornik Math. 188 (1997). Then we describe some covering properties of our manifolds, and show that many of them are hyperelliptic. Finally, we completely classify Kim-Kostrikin manifolds, and determine their Seifert invariants.
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