On periodic Takahashi manifolds

2001/04/24 by Michele Mulazzani, Mulazzani, Michele
Mathematics · #57M12 #57R65 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M12 #msc:57R65

paper · pdf · doi:10.48550/arxiv.math/0104224

12 pages, 5 figures. To appear in Tsukuba Journal of Mathematics

arxiv created 2001/04/24 · arxiv updated 2009/11/30

Abstract

In this paper we show that periodic Takahashi 3-manifolds are cyclic coverings of the connected sum of two lens spaces (possibly cyclic coverings of the 3-sphere), branched over knots. When the base space is a 3-sphere, we prove that the associated branching set is a two-bridge knot of genus one, and we determine its type. Moreover, a geometric cyclic presentation for the fundamental groups of these manifolds is obtained in several interesting cases, including the ones corresponding to the branched cyclic coverings of the 3-sphere.

Related

• Generalized Takahashi manifolds
• The many faces of cyclic branched coverings of 2-bridge knots and links
• Genus one 1-bridge knots and Dunwoody manifolds
• Cyclic generalizations of two hyperbolic icosahedral manifolds
• Cyclic branched covers of alternating knots and L-spaces