Abstract
Let f1: M1 → M2 be a homotopic equivalence and N ⊂ m2 a subvariety of codimensionality one. In this paper we indicate the conditions under which there is a mapping f2 ~ f1 such that the variety f2 −1(N) is simply homotopically equivalent to the variety N.
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F. T. Farrel, “The obstruction to fibering a manifold over a circle,” Bull. Amer. Math. Soc.,73, No. 5, 737–740 (1967).
F. T. Farrel and W. C. Hsiang, “A geometric interpretation of the Kunneth formula for algebraic K-theory,” Bull. Amer. Math. Soc.,74, No. 3, 548–553 (1968).
J. Milnor, “Whitehead torsion,” in Matematika, 11:1, 1–37 (1967).
W. C. Hsiang, “A splitting theorem and the Kunneth formula in algebraic K-theory,” Lecture Notes in Mathematics, No. 108, 72–77.
V. L. Golo, “Realization of Whitehead torsion and the discriminants of bilinear forms,” Dokl. Akad. Nauk SSSR,183, No. 6, 1247–1249 (1968).
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Translated from Matematicheskie Zametki, Vol. 12, No. 2, pp. 167–175, August, 1972.
In conclusion the author wishes to express his deep gratitude to A. S. Mishcheriko who directed the preparation of this paper.
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Shlosman, S.B. Subvarieties of codimensionality one and of simple homotopic type. Mathematical Notes of the Academy of Sciences of the USSR 12, 536–540 (1972). https://doi.org/10.1007/BF01095014
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DOI: https://doi.org/10.1007/BF01095014