Abstract
AbstractWe prove that if K is a nontrivial null-homotopic knot in a closed oriented 3–manfiold Y such that
$Y-K$
does not have an
$S^1\times S^2$
summand, then the zero surgery on K does not have an
$S^1\times S^2$
summand. This generalises a result of Hom and Lidman, who proved the case when Y is an irreducible rational homology sphere.
Publisher
Cambridge University Press (CUP)
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1. Property G and the 4-genus;Transactions of the American Mathematical Society, Series B;2024-01-12