Dehn surgery on knots in S^3 producing Nil Seifert fibred 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^3, 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^3 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^3.

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