We show that if a knot has a minimal spanning surface that admits certain Gabai disks, then a manifold obtained by ±1-Dehn surgery along the knot has infinite fundamental group. As one of the applications we extend and simplify a recent result of Menasco and Zhang that closed 3-braid knots have Property P. Other applications are given. © 2004 Elsevier B.V. All rights reserved.
Publication Source (Journal or Book title)
Topology and its Applications
Dasbach, O., & Li, T. (2004). Property P for knots admitting certain Gabai disks. Topology and its Applications, 142 (1-3), 113-129. https://doi.org/10.1016/j.topol.2003.11.010