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Existence of $ \pi\sb 1$-negligible embeddings in $ 4$-manifolds. A correction to Theorem 10.5 of Freedmann and Quinn


Author: Richard Stong
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
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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 [Enhancements On Off] (What's this?)

  • [FK] M. Freedman and R. Kirby, A geometric proof of Rochlin's theorem, Proc. Sympos. Pure Math., vol. 32, Amer. Math. Soc., Providence, RI, 1978, pp. 85-98. MR 520525 (80f:57015)
  • [FQ] M. Freedman and F. Quinn, Topology of $ 4$-manifold, Princeton Univ. Press, Princeton, NJ, 1990. MR 1201584 (94b:57021)
  • [KM] M. A. Kervaire and J. W. Milnor, On $ 2$-spheres in $ 4$-manifold, Proc. Nat. Acad. Sci. U.S.A. 47 (1961), 1651-1657. MR 0133134 (24:A2968)
  • [S] R. Stong, Uniqueness of $ {\pi _1}$-negligible embeddings in $ 4$-manifolds: A correction to theorem 10.5 of Freedman and Quinn, Topology (to appear). MR 1241868 (94m:57042)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1215031-9
Keywords: $ 4$-manifolds
Article copyright: © Copyright 1994 American Mathematical Society

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