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Cosmetic surgeries on genus one knots. (English) Zbl 1130.57020
Summary: In this paper, we prove that there are no truly cosmetic surgeries on genus one classical knots. If the two surgery slopes have the same sign, we give the only possibilities of reflectively cosmetic surgeries. The result is an application of Heegaard Floer theory and number theory.

##### MSC:
 57M27 Invariants of knots and $$3$$-manifolds (MSC2010) 57R58 Floer homology 53D40 Symplectic aspects of Floer homology and cohomology
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