Affiliation:
1. Dipartimento di Matematica, Università di Bologna Piazza di Porta San Donato, 5–40127 BOLOGNA, Italy
Abstract
In this paper we show that all Lins-Mandel spaces S (b, l, t, c) are branched cyclic coverings of the 3-sphere. When the space is a 3-manifold, the branching set of the covering is a two-bridge knot or link of type (l, t) and otherwise is a graph with two vertices joined by three edges (a θ-graph). In the latter case the singular set of the space is always composed by two points with homeomorphic links. The first homology groups of the Lins-Mandel manifolds are computed when t=1 and when the branching set is a knot of genus one. Furthermore the family of spaces has been extended in order to contain all branched cyclic coverings of two-bridge knots or links.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
3 articles.
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1. COMPLEXITY, HEEGAARD DIAGRAMS AND GENERALIZED DUNWOODY MANIFOLDS;Journal of the Korean Mathematical Society;2010-05-01
2. Genus one 1-bridge knots and Dunwoody manifolds;Forum Mathematicum;2001-01-05
3. On the cyclic coverings of the knot 52;Proceedings of the Edinburgh Mathematical Society;1999-10