Homology spheres yielding lens spaces

Abstract

It is known by the author that there exist 20 families of Dehn surgeries in the Poincaré homology sphere yielding lens spaces. In this paper, we give the concrete knot diagrams of the families and extend them to families of lens space surgeries in Brieskorn homology spheres. We illustrate families of lens space surgeries in $\Sigma (2,3,6n\pm 1)$ and $\Sigma (2,2s+1,2(2s+1)n\pm 1)$ and so on. As other examples, we give lens space surgeries in graph homology spheres, which are obtained by splicing two Brieskorn homology spheres.

40 pages and 45 figures, to appear in Proceedings of the Gokova Geometry-Topology Conference 2017

References in corpus (3)

• Lens space surgeries and L-space homology spheres
• Some knots with surgeries yielding lens spaces
• A complete list of lens spaces constructed by Dehn surgery I