Abstract.
In this paper, we define and investigate \( \mathbb{Z}_2 \)-homology cobordism invariants of \( \mathbb{Z}_2 \)-homology 3-spheres which turn out to be related to classical invariants of knots. As an application, we show that many lens spaces have infinite order in the \( \mathbb{Z}_2 \)-homology cobordism group and we prove a lower bound for the slice genus of a knot on which integral surgery yields a given \( \mathbb{Z}_2 \)-homology sphere. We also give some new examples of 3-manifolds which cannot be obtained by integral surgery on a knot.
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Received: May 7, 2001
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Bohr, C., Lee, R. Homology cobordism and classical knot invariants. Comment. Math. Helv. 77, 363–382 (2002). https://doi.org/10.1007/s00014-002-8344-0
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DOI: https://doi.org/10.1007/s00014-002-8344-0