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Line bundles over framed manifolds. (English) Zbl 0311.55011


MSC:

55R25 Sphere bundles and vector bundles in algebraic topology
57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
57M10 Covering spaces and low-dimensional topology
57R90 Other types of cobordism
55R50 Stable classes of vector space bundles in algebraic topology and relations to \(K\)-theory
57T15 Homology and cohomology of homogeneous spaces of Lie groups
55Q50 \(J\)-morphism
55R10 Fiber bundles in algebraic topology
55R40 Homology of classifying spaces and characteristic classes in algebraic topology
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References:

[1] Adams, J. F.: On the Groups J (X) IV. Topology5, 21-71 (1966) · Zbl 0145.19902 · doi:10.1016/0040-9383(66)90004-8
[2] Adams, J. F.: The Kahn-Priddy Theorem. Proc. Cambridge philos. Soc.73, 45-55 (1973) · Zbl 0245.55015 · doi:10.1017/S0305004100047459
[3] Atiyah, M. F., Smith, L.: Compact Lie Groups and the Stable Homotopy of Spheres. Topology (to appear) · Zbl 0282.55008
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[7] Mosher, R.: Some Stable Homotopy of Complex Projective Space. Topology7, 179-193 (1968) · Zbl 0172.25103 · doi:10.1016/0040-9383(68)90026-8
[8] Quillen, D. G.: The Adams Conjecture. Topology10, 67-80 (1971) · Zbl 0219.55013 · doi:10.1016/0040-9383(71)90018-8
[9] Smith, L.: An application of Riemannian Geometry, to Stable Homotopy Theory. Yale University Preprint 1972
[10] Smith, L.: Framings of Sphere Bundles over Spheres, etc. Aarhus University Preprint 1973
[11] Smith, L.: Thee Invariant and Finite Coverings. Aarhus University Preprint 1974
[12] Stong, R. E.: Notes on Cobordism Theory. Princeton. Princeton University Press 1966 · Zbl 0144.22702
[13] Toda, H.: A Survey of Homotopy Theory; translated by Mi-Soo Bae Smith. Advances Math.10, 417-455 (1973) · Zbl 0262.55012 · doi:10.1016/0001-8708(73)90124-2
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