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Classification of certain 6-manifolds

Published online by Cambridge University Press:  24 October 2008

P. E. Jupp
Affiliation:
University of Geneva†

Extract

In (13) Wall classified up to diffeomorphism, PL-homeomorphism, topological homeomorphism, and homotopy equivalence all closed, oriented, 1-connected smooth (or PL) 6-manifolds with torsion-free homology and vanishing second Stiefel-Whitney class. This paper extends these classifications to all closed, oriented, 1-connected topological 6-manifolds with torsion-free homology. The method differs from that of (13) but uses two special cases of Wall's classification.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

(1)Boardman, J. M. and Vogt, R. M.Homotopy-everything H-spaces. Bull. Amer. Math. Soc. 74 (1968), 11171122.CrossRefGoogle Scholar
(2)Haefliger, A. and Poenaru, V.La classification des immersions combinatoires. Publ. Math. I.H.E.S. 23 (1964), 7591.CrossRefGoogle Scholar
(3)Hilton, P. J.On the homotopy groups of the union of spheres. J. London Math. Soc. 30 (1955), 154172.CrossRefGoogle Scholar
(4)Hirsch, M. W.Immersions of manifolds. Trans. Amer. Math. Soc. 93 (1959), 242276.CrossRefGoogle Scholar
(5)Hirzebruch, F.Topological methods in algebraic geometry, 3rd ed. (Springer-Verlag, Berlin, 1966.)Google Scholar
(6)Husemoller, D.Fibre bundles (McGraw-Hill, New York, 1966).CrossRefGoogle Scholar
(7)James, I. M. and Whitehead, J. H. C.The homotopy theory of sphere bundles over spheres (I). Proc. London Math. Soc. (3), 4 (1954), 196218.CrossRefGoogle Scholar
(8)Kirby, R. C. and Siebenmann, L. C.On the triangulation of manifolds and the Hauptvermutung. Bull. Amer. Math. Soc. 75 (1969), 742749.CrossRefGoogle Scholar
(9)Lees, J. A.Immersions and surgeries of topological manifolds. Bull. Amer. Math. Soc. 75 (1969), 529534.CrossRefGoogle Scholar
(10)Siebenmann, L. C.A report on topological manifolds. Proceedings I.C.M. Nice (1970).Google Scholar
(11)Steer, B.Generalized Whitehead products. Quart. J. Math. Oxford Ser. (2), 14 (1963), 2940.CrossRefGoogle Scholar
(12)Tamura, I.On Pontrjagin classes and homotopy types of manifolds. J. Math. Soc. Japan 9 (1957), 250262.CrossRefGoogle Scholar
(13)Wall, C. T. C.Classification problems in differential topology. V. On certain 6-manifolds. Invent. Math. 1 (1966), 335374.CrossRefGoogle Scholar
(14)Wall, C. T. C.Surgery on compact manifolds (Academic Press, London, 1970).Google Scholar