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On Homotopy Domination

Published online by Cambridge University Press:  20 November 2018

Sławomir Kwasik
Sławomir Kwasik*
Affiliation:
Mathematisches Institut, Universität Heidelberg, 6900 Heidelberg, Im Neuenheimer Feld 288, West Germany
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Abstract

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A short proof of the following result of Bernstein and Ganea is given:

“Let X be a topological space which is homotopy dominated by a closed connected n-dimensional manifold M. If Hn (X; Z2 ) ≠ 0 then X has the homotopy type of M”.

It is also shown that the manifold in this theorem can be replaced by a Poincaré complex.

Keywords

55P1057P10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 4 , 01 December 1984 , pp. 448 - 451
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Berstein, I. and Ganea, T., Remark on spaces dominated by manifolds, Fund. Math. 47, (1959), 45-56.10.4064/fm-47-1-45-56CrossRefGoogle Scholar
2. Browder, W., Poincaré Spaces, Their Normal Fibrations and Surgery, Inventiones Math. 17, (1972), 0191-202.10.1007/BF01425447CrossRefGoogle Scholar
3. Ferry, S., Homotoping ε-maps to homeomorphisms, Amer. J. Math. 101, (1979), 567-582.10.2307/2373798CrossRefGoogle Scholar
4. Ganea, T., On ε-maps onto manifolds, Fund. Math. 47, (1959), 35-44.10.4064/fm-47-1-35-44CrossRefGoogle Scholar
5. Kirby, R. C. and Siebenmann, L. C., On the triangulation of manifolds and Hauptvermutung, Bull. Amer. Math. Soc. 75, (1969), 742-749.10.1090/S0002-9904-1969-12271-8CrossRefGoogle Scholar
6. Milnor, J., Spaces having the homotopy type of a CW-complex, Trans. Amer. Math. Soc. 90, (1959), 272-280.Google Scholar
7. Milnor, J. and Stasheff, J., Characteristic classes, Ann. Math. Studies 76, Princeton Univ. Press 1974.Google Scholar
8. Schafer, J. A., Topological Pontriagin Classes, Comment. Math. Helv. 45, (1970), 315-332.10.1007/BF02567335CrossRefGoogle Scholar
9. Wall, C. T. C., Poincaré complexes, Ann. of Math. 86 (1967), 213-245.10.2307/1970688CrossRefGoogle Scholar