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By Efstratia Kalfagianni


Abstract. We prove that a crossing circle L of a fibered knot K bounds a disc in the complement of K, if and only if there is a crossing change supported on L that doesn't change the isotopy class of K. We also sow that if a knot K is n-adjacent to a fibered knot K0, for some n> 1, then either the genus of K is larger that of K0 or K is isotopic to K0. This statement leads to criteria for detecting non-fibered knots and it has some applications in the theory of finite type 3-manifold invariants. AMS classification numbers: 57M25, 57M27, 57M50. Keywords: crossing change, commutator length of a Dehn twist, fibered knot, mapping class group, Heegaard splitting, Thurston norm

Year: 2008
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