Skip to main content Accessibility help
×
Home

Classification of certain 6-manifolds

  • P. E. Jupp (a1)

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.

Copyright

References

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

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed