A GOOD PRESENTATION OF (-2, 3, 2s + 1)-TYPE PRETZEL KNOT GROUP AND ℝ-COVERED FOLIATION

Abstract

Let Ks be a (-2, 3, 2s + 1)-type pretzel knot (s ≧ 3) and EKs(p/q) be a closed manifold obtained by Dehn surgery along Ks with a slope p/q. We prove that if q > 0, p/q ≧ 4s + 7 and p is odd, then EKs(p/q) cannot contain an ℝ-covered foliation. This result is an extended theorem of a part of works of Jun for (-2, 3, 7)-pretzel knot.