English

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

R2 v1 2026-06-21T12:01:23.601Z