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]**M. Freedman and R. Kirby,*A geometric proof of Rochlin's theorem*, Proc. Sympos. Pure Math., vol. 32, Part 2, Amer. Math. Soc., Providence, R. I., 1978, pp. 85-98. MR**520525 (80f:57015)****[2]**K. Kobayashi,*On a homotopy version of*4-*dimensional Whitney's lemma*, Math. Seminar Notes Kobe Univ.**5**(1977), 109-116. MR**0458431 (56:16634)****[3]**Y. Matsumoto,*Secondary intersectional properties of*4-*manifolds and Whitney's trick*, Proc. Sympos. Pure Math., vol. 32, Part 2, Amer. Math. Soc., Providence, R. I., 1978, pp. 99-107. MR**520526 (80e:57017)****[4]**J. Milnor,*Lectures on the h-cobordism theorem*, Math. Notes, vol. 1, Princeton Univ. Press, Princeton, N. J., 1965. MR**0190942 (32:8352)**

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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