On periodic Takahashi manifolds

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 S 3 ), 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 S 3 .Mathematics Subject Classification 2000: Primary 57M12, 57R65; Secondary 20F05, 57M05, 57M25.

Twisted Face-Pairing 3-Manifolds Which Are Hyperbolic

“…Let us denoted by L 2n the 2n-component link of the Figure 3, which is a closed chain of 2n unknotted components, with surgery coefficients [8], [10], and [11]. From now on, without loss of generality, we assume that: gcd(p, q) = 1, gcd(r, s) = 1 and p, r ≥ 0.…”

“…In [8], [10], and [11] they gave finite presentations of the fundamental group of the periodic Takahashi manifold M n ( …”

Strongly-cyclic branched coverings of knots via (g, 1)-decompositions

“…. In [8] it is proved that generalized periodic Takahashi manifolds are strongly-cyclic branched coverings of certain knots in connected sums of lens spaces. That result is improved by the following.…”

On Branched Coverings of Lens Spaces

“…These presentations were considered in [5,13,21] for p i = p, i = q and k i = k, and in [12] for p i = i = 1 and…”