The lens space realization problem

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 th...

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Bibliographic Details
Published in:Annals of mathematics 2013-03, Vol.177 (2), p.449-511
Main Author: Greene, Joshua Evan
Format: Article
Language:English
Subjects:
Claws
Continued fractions
Integers
Mathematical lattices
Mathematical manifolds
Mathematical theorems
Mathematical vectors
Topological spaces
Vertices
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Summary: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. They are primarily combinatorial in nature.
ISSN:0003-486X
DOI:10.4007/annals.2013.177.2.3