Irreducible 3-manifolds that cannot be obtained by 0-surgery on a knot
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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2018
- DOI:
- 10.48550/arXiv.1802.08620
- arXiv:
- arXiv:1802.08620
- Bibcode:
- 2018arXiv180208620H
- Keywords:
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- Mathematics - Geometric Topology
- E-Print:
- 18 pages, 8 figures