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Some results on extension of maps and applications

  • Carlos Biasi (a1), Alice K. M. Libardi (a2), Thiago de Melo (a2) and Edivaldo L. dos Santos (a3)

Abstract

This paper concerns extension of maps using obstruction theory under a non-classical viewpoint. It is given a classification of homotopy classes of maps and as an application it is presented a simple proof of a theorem by Adachi about equivalence of vector bundles. Also it is proved that, under certain conditions, two embeddings are homotopic up to surgery if and only if the respective normal bundles are SO-equivalent.

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Dedicated to Professor Gilberto Loibel, in memorian.

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References

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1Adachi, M.. A remark on submersions and immersions with codimension one or two. J. Math. Kyoto Univ. 9 (1969), 393404.
2Kervaire, M. A. and Milnor, J. W.. Groups of homotopy spheres. I. Ann. Math. 77 (1963), 504537.
3Loibel, G. F. and Pinto, R. C. E.. c-equivalence of embeddings is different from equivalence and bordism of pairs. Bol. Soc. Bras. Mat. 13 (1982), 6367.
4Milnor, J., A procedure for killing homotopy groups of differentiable manifolds. In: Proc. Symp. Pure Math., Vol. III, Am. Math. Soc., (1961) 3955.
5Spanier, E. H.. Algebraic topology (New York: McGraw-Hill, 1966).

Keywords

MSC classification

Some results on extension of maps and applications

  • Carlos Biasi (a1), Alice K. M. Libardi (a2), Thiago de Melo (a2) and Edivaldo L. dos Santos (a3)

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