Dehn Surgery on Knots in S³ Producing Nil Seifert Fibered Spaces

Abstract

We prove that there are exactly 6 Nil Seifert fibred spaces which can be obtained by Dehn surgeries on non-trefoil knots in S, with {60, 144, 156, 288, 300} as the exact set of all such surgery slopes up to taking the mirror images of the knots. We conjecture that there are exactly 4 specific hyperbolic knots in S which admit Nil Seifert fibred surgery. We also give some more general results and a more general conjecture concerning Seifert fibred surgeries on hyperbolic knots in S.