2005/06/23 by Brendan Owens, Owens, Brendan
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT
paper · pdf · doi:10.48550/arxiv.math/0506485
26 pages, 13 figures (xypic)
arxiv created 2005/06/23 · arxiv updated 2009/12/01
We use Heegaard Floer homology to obtain bounds on unknotting numbers. This is a generalisation of Ozsvath and Szabo's obstruction to unknotting number one. We determine the unknotting numbers of 910, 913, 935, 938, 1053, 10101 and 10120; this completes the table of unknotting numbers for prime knots with crossing number nine or less. Our obstruction uses a refined version of Montesinos' theorem which gives a Dehn surgery description of the branched double cover of a knot.