Cosmetic crossings of genus one knots

Details Cosmetic crossings of genus one knots Cosmetic crossings of genus one knots

2011-07-11

arxiv.org/abs/1107.2034v1

Mathematics

Geometric Topology

9 pages, 5 Figures

Scientific paper

We show that for genus one knots the Alexander polynomial and the homology of the double cover branching over the knot provide obstructions to cosmetic crossings. As an application we prove the nugatory crossing conjecture for the negatively twisted, positive Whitehead doubles of all knots. We also verify the conjecture for several families of pretzel knots and all genus one knots with up to 10 crossings.

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