Cosmetic crossing changes of fibered knots

Details Cosmetic crossing changes of fibered knots Cosmetic crossing changes of fibered knots

2006-10-14

arxiv.org/abs/math/0610440v4

Mathematics

Geometric Topology

Completely rewritten and shortened. To appear in J. Reine Angew. Math.(Crelle's Journal)

Scientific paper

We prove the nugatory crossing conjecture for fibered knots. We also show
that if a knot $K$ is $n$-adjacent to a fibered knot $K'$, for some $n>1$, then
either the genus of $K$ is larger than that of $K'$ or $K$ is isotopic to $K'$.

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