On periodic Takahashi manifolds (Q1848088)

A Takahashi manifold is a closed orientable 3-manifold, obtained by Dehn surgery on \(S^3\). The surgery is performed along a certain link with \(2n\) components arranged in a circle, each component linked simply with its 2 neighbours. Periodic Takahashi manifolds arise when the surgery coefficients are alternately \(p/q\) and \(r/s\). The author shows that a periodic Takahashi manifold is an \(n\)-fold branched cyclic covering of the connected sum of two lens spaces. The branch set is a knot which is also described in the paper. Geometric presentations for the fundamental groups of some interesting examples of these manifolds are also given.