Existence of -negligible embeddings in -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* -*manifolds*, Princeton Univ. Press, Princeton, NJ, 1990, which analyze when one can find a connected sum decomposition of a -manifold or a -negligible embedding in a -manifold respectively. In particular this gives a correction to the definition of the -dimensional Kervaire-Milnor invariant. We also define this invariant in a slightly more general context.

**[FK]**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****[FQ]**Michael H. Freedman and Frank Quinn,*Topology of 4-manifolds*, Princeton Mathematical Series, vol. 39, Princeton University Press, Princeton, NJ, 1990. MR**1201584****[KM]**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**0133134****[S]**Richard Stong,*Uniqueness of 𝜋₁-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**, https://doi.org/10.1016/0040-9383(93)90046-X

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1215031-9

Keywords:
-manifolds

Article copyright:
© Copyright 1994
American Mathematical Society