Irreducible 3-manifolds that cannot be obtained by 0-surgery on a knot

Matthew Hedden, Min Hoon Kim, Thomas E. Mark, Kyungbae Park

Published 2018-02-23Version 1

We give infinitely many examples of closed, orientable, irreducible 3-manifolds $M$ such that $b_1(M)=1$ and $\pi_1(M)$ has weight 1, but $M$ is not the result of Dehn surgery along a knot in the 3-sphere. This answers a question of Aschenbrenner, Friedl and Wilton, and provides the first examples of irreducible manifolds with $b_1=1$ that are known not to be surgery on a knot in the 3-sphere. We further show that our examples are not even homology cobordant to any manifold obtained by Dehn surgery along a knot in the 3-sphere, or any Seifert fibered 3-manifold.