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

Hedden, Matthew; Kim, Min Hoon; Mark, Thomas; Park, Kyungbae

doi:10.1090/tran/7786

Irreducible 3-manifolds that cannot be obtained by 0-surgery on a knot
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by Matthew Hedden, Min Hoon Kim, Thomas E. Mark and Kyungbae Park PDF

Trans. Amer. Math. Soc. 372 (2019), 7619-7638 Request permission

Abstract:

We give two infinite families of 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. One family consists of Seifert fibered 3-manifolds, while each member of the other family is not even homology cobordant to any Seifert fibered 3-manifold. None of our examples are homology cobordant to any manifold obtained by Dehn surgery along a knot in the 3-sphere.

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