Abstract
We give two infinite families of examples of closed, orientable, irreducible 3-manifolds M M such that b 1 ( M ) = 1 b_1(M)=1 and π 1 ( M ) \pi _1(M) has weight 1, but M 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 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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