Existence of 𝜋₁-negligible embeddings in 4-manifolds. A correction to Theorem 10.5 of Freedmann and Quinn

Stong, Richard

doi:10.1090/S0002-9939-1994-1215031-9

Existence of $\pi _ 1$-negligible embeddings in $4$-manifolds. A correction to Theorem 10.5 of Freedmann and Quinn
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Proc. Amer. Math. Soc. 120 (1994), 1309-1314 Request permission

Abstract:

The purpose of this note is to provide a correction to the existence part of Theorems 10.3 and 10.5 of Topology of $4$-manifolds, Princeton Univ. Press, Princeton, NJ, 1990, which analyze when one can find a connected sum decomposition of a $4$-manifold or a ${\pi _1}$-negligible embedding in a $4$-manifold respectively. In particular this gives a correction to the definition of the $4$-dimensional Kervaire-Milnor invariant. We also define this invariant in a slightly more general context.

References

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Michael H. Freedman and Frank Quinn, Topology of 4-manifolds, Princeton Mathematical Series, vol. 39, Princeton University Press, Princeton, NJ, 1990. MR 1201584
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Richard Stong, Uniqueness of $\pi _1$-negligible embeddings in $4$-manifolds: a correction to Theorem 10.5 of Topology of 4-manifolds [Princeton Univ. Press, Princeton, NJ, 1990; MR1201584 (94b:57021)] by M. H. Freedman and F. Quinn, Topology 32 (1993), no. 4, 677–699. MR 1241868, DOI 10.1016/0040-9383(93)90046-X