The lens space realization problem

Abstract

We determine the lens spaces that arise by integer Dehn surgery along a knot in the three-sphere. Specifically, if surgery along a knot produces a lens space, then there exists an equivalent surgery along a Berge knot with the same knot Floer homology groups. This leads to sharp information about the genus of such a knot. The arguments rely on tools from Floer homology and lattice theory, and are primarily combinatorial in nature.

52 pages, 1 figure

References in corpus (4)

• Lens space surgeries and L-space homology spheres
• Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology
• On closed 3-braids with unknotting number one
• A complete list of lens spaces constructed by Dehn surgery I

Cited by in corpus (1)

• H(2)-Unknotting Operation Related to 2-Bridge Links