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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Whitney’s trick for three $2$-dimensional homology classes of $4$-manifolds
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by Masayuki Yamasaki PDF
Proc. Amer. Math. Soc. 75 (1979), 365-371 Request permission

Abstract:

In his recent paper, Y. Matsumoto has defined a triple product of 2-homology classes of simply-connected oriented 4-manifolds, when the intersection numbers are zero. In the present paper, the author establishes that three 2-homology classes can be homotopically separated if the intersection numbers and the triple product vanish.
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
  • Kazuaki Kobayashi, On a homotopy version of $4$-dimensional Whitney’s lemma, Math. Sem. Notes Kobe Univ. 5 (1977), no. 1, 109–116. MR 458431
  • Yukio Matsumoto, Secondary intersectional properties of $4$-manifolds and Whitney’s trick, 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. 99–107. MR 520526
  • John Milnor, Lectures on the $h$-cobordism theorem, Princeton University Press, Princeton, N.J., 1965. Notes by L. Siebenmann and J. Sondow. MR 0190942
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 75 (1979), 365-371
  • MSC: Primary 57N15
  • DOI: https://doi.org/10.1090/S0002-9939-1979-0532167-8
  • MathSciNet review: 532167