Fibered knots and Property 2R

Details Fibered knots and Property 2R Fibered knots and Property 2R

2009-01-15

arxiv.org/abs/0901.2319v1

Mathematics

Geometric Topology

18 pages, 4 figures

Scientific paper

It is shown, using sutured manifold theory, that if there are any 2-component counterexamples to the Generalized Property R Conjecture, then any knot of least genus among components of such counterexamples is not a fibered knot. The general question of what fibered knots might appear as a component of such a counterexample is further considered; much can be said about the monodromy of the fiber, particularly in the case in which the fiber is of genus two.

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