Existence of $\pi _ 1$-negligible embeddings in $4$-manifolds. A correction to Theorem 10.5 of Freedmann and Quinn
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- by Richard Stong PDF
- 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
- Michael Freedman and Robion Kirby, A geometric proof of Rochlin’s theorem, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976) Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, R.I., 1978, pp. 85–97. MR 520525
- Michael H. Freedman and Frank Quinn, Topology of 4-manifolds, Princeton Mathematical Series, vol. 39, Princeton University Press, Princeton, NJ, 1990. MR 1201584
- Michel A. Kervaire and John W. Milnor, On $2$-spheres in $4$-manifolds, Proc. Nat. Acad. Sci. U.S.A. 47 (1961), 1651–1657. MR 133134, DOI 10.1073/pnas.47.10.1651
- 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
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 1309-1314
- MSC: Primary 57N35; Secondary 57N13, 57Q25
- DOI: https://doi.org/10.1090/S0002-9939-1994-1215031-9
- MathSciNet review: 1215031