Cosmetic surgeries on genus one knots

Details Cosmetic surgeries on genus one knots Cosmetic surgeries on genus one knots

2005-12-13

arxiv.org/abs/math/0512253v2

Algebr. Geom. Topol. 6 (2006) 1491-1517

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 4 October 2006

Scientific paper

10.2140/agt.2006.6.1491

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.

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