Whitney's trick for three -dimensional homology classes of -manifolds

Author:
Masayuki Yamasaki

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

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Abstract | References | Similar Articles | Additional Information

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.

**[1]**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****[2]**Kazuaki Kobayashi,*On a homotopy version of 4-dimensional Whitney’s lemma*, Math. Sem. Notes Kobe Univ.**5**(1977), no. 1, 109–116. MR**0458431****[3]**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****[4]**John Milnor,*Lectures on the ℎ-cobordism theorem*, Notes by L. Siebenmann and J. Sondow, Princeton University Press, Princeton, N.J., 1965. MR**0190942**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1979-0532167-8

Keywords:
Matsumoto triple,
Whitney's trick

Article copyright:
© Copyright 1979
American Mathematical Society