## Abstract

We give two infinite families of examples of closed, orientable, irreducible 3-manifolds M such that b_{1}(M) = 1 and π1(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.

Original language | English |
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Pages (from-to) | 7619-7638 |

Number of pages | 20 |

Journal | Transactions of the American Mathematical Society |

Volume | 372 |

Issue number | 11 |

DOIs | |

State | Published - 1 Dec 2019 |

### Bibliographical note

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