Fibered knots and Property 2R
Geometric Topology
2009-01-16 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0901.2319,
title = {Fibered knots and Property 2R},
author = {Martin Scharlemann and Abigail Thompson},
journal= {arXiv preprint arXiv:0901.2319},
year = {2009}
}
Comments
18 pages, 4 figures