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A note on the $ bP$-component of $ (4n-1)$-dimensional homotopy spheres


Author: Stephan Stolz
Journal: Proc. Amer. Math. Soc. 99 (1987), 581-584
MSC: Primary 57R60; Secondary 57R20, 57R55
MathSciNet review: 875404
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Abstract: The $ bP$-component of a $ \left( {4n - 1} \right)$-dimensional homotopy sphere $ \Sigma \in {\theta _{4n - 1}} \cong b{P_{4n}} \oplus {\left( {{\text{Co}}\ker J} \right)_{4n - 1}}$ bounding a spin manifold $ M$ is shown to be computable in terms of the signature and the decomposable Pontrjagin numbers of $ M$.


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  • [1] G. Brumfiel, On the homotopy groups of 𝐵𝑃𝐿 and 𝑃𝐿/𝑂, Ann. of Math. (2) 88 (1968), 291–311. MR 0234458
  • [2] G. Brumfiel, Homotopy equivalences of almost smooth manifolds, Comment. Math. Helv. 46 (1971), 381–407. MR 0305419
  • [3] James Eells Jr. and Nicolaas Kuiper H., An invariant for certain smooth manifolds, Ann. Mat. Pura Appl. (4) 60 (1962), 93–110. MR 0156356
  • [4] Friedrich Hirzebruch, Topological methods in algebraic geometry, Classics in Mathematics, Springer-Verlag, Berlin, 1995. Translated from the German and Appendix One by R. L. E. Schwarzenberger; With a preface to the third English edition by the author and Schwarzenberger; Appendix Two by A. Borel; Reprint of the 1978 edition. MR 1335917
  • [5] Michel A. Kervaire and John W. Milnor, Groups of homotopy spheres. I, Ann. of Math. (2) 77 (1963), 504–537. MR 0148075
  • [6] R. Lampe, Diffeomorphismen auf Sphären und die Milnor-Paarung, Diplomarbeit, Mainz, 1981.
  • [7] John W. Milnor and James D. Stasheff, Characteristic classes, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974. Annals of Mathematics Studies, No. 76. MR 0440554
  • [8] Stephan Stolz, Hochzusammenhängende Mannigfaltigkeiten und ihre Ränder, Lecture Notes in Mathematics, vol. 1116, Springer-Verlag, Berlin, 1985 (German). With an English introduction. MR 871476
  • [9] C. T. C. Wall, Classification of (𝑛-1)-connected 2𝑛-manifolds, Ann. of Math. (2) 75 (1962), 163–189. MR 0145540
  • [10] C. T. C. Wall, Classification problems in differential topology. VI. Classification of (𝑠-1)-connected (2𝑠+1)-manifolds, Topology 6 (1967), 273–296. MR 0216510

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0875404-7
Article copyright: © Copyright 1987 American Mathematical Society