Alternating knots satisfy strong property P

Suppose a manifold is produced by finite Dehn surgery on a non-torus alternating knot for which Seifert's algorithm produces a checkerboard surface. By demonstrating that it contains an essential lamination, we prove that such a manifold has ℝ³ as universal cover and, consequently, is irreducible and has infinite fundamental group. Together with previous work of Roberts, who proved this result in the case of alternating knots for which Seifert's algorithm does not produce a checkerboard surface, and Moser, who classified the manifolds produced by surgery on torus knots, this paper completes the proof that alternating knots satisfy Strong Property P.