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On the existence of immersions and submersions. (English) Zbl 0169.26101


Keywords:

topology
Full Text: DOI

References:

[1] Armand Borel, Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. of Math. (2) 57 (1953), 115 – 207 (French). · Zbl 0052.40001 · doi:10.2307/1969728
[2] Raoul Bott, The stable homotopy of the classical groups, Ann. of Math. (2) 70 (1959), 313 – 337. · Zbl 0129.15601 · doi:10.2307/1970106
[3] W. Browder, J. Levine, and G. R. Livesay, Finding a boundary for an open manifold, Amer. J. Math. 87 (1965), 1017 – 1028. · Zbl 0134.42801 · doi:10.2307/2373259
[4] Samuel Feder, Immersions and embeddings in complex projective spaces, Topology 4 (1965), 143 – 158. · Zbl 0151.32301 · doi:10.1016/0040-9383(65)90062-5
[5] Ioan James and Emery Thomas, Submersions and immersions of manifolds, Invent. Math. 2 (1967), 171 – 177. · Zbl 0146.19803 · doi:10.1007/BF01425511
[6] André Haefliger and Morris W. Hirsch, On the existence and classification of differentiable embeddings, Topology 2 (1963), 129 – 135. · Zbl 0113.38607 · doi:10.1016/0040-9383(63)90028-4
[7] Morris W. Hirsch, Immersions of manifolds, Trans. Amer. Math. Soc. 93 (1959), 242 – 276. · Zbl 0113.17202
[8] Morris W. Hirsch, On imbedding differentiable manifolds in euclidean space, Ann. of Math. (2) 73 (1961), 566 – 571. · Zbl 0123.16701 · doi:10.2307/1970318
[9] S. D. Liao, On the theory of obstructions of fiber bundles, Ann. of Math. (2) 60 (1954), 146 – 191. · Zbl 0057.15401 · doi:10.2307/1969704
[10] Mark Mahowald, On obstruction theory in orientable fiber bundles, Trans. Amer. Math. Soc. 110 (1964), 315 – 349. · Zbl 0128.16805
[11] Mark E. Mahowald and Franklin P. Peterson, Secondary cohomology operations on the Thom class, Topology 2 (1963), 367 – 377. · Zbl 0166.19502 · doi:10.1016/0040-9383(63)90016-8
[12] W. S. Massey, On the Stiefel-Whitney classes of a manifold, Amer. J. Math. 82 (1960), 92 – 102. · Zbl 0089.39301 · doi:10.2307/2372878
[13] W. S. Massey, On the Stiefel-Whitney classes of a manifold. II, Proc. Amer. Math. Soc. 13 (1962), 938 – 942. · Zbl 0109.15902
[14] W. S. Massey and F. P. Peterson, On the dual Stiefel-Whitney classes of a manifold, Bol. Soc. Mat. Mexicana (2) 8 (1963), 1 – 13. · Zbl 0121.18005
[15] John Milnor, Construction of universal bundles. II, Ann. of Math. (2) 63 (1956), 430 – 436. · Zbl 0071.17401 · doi:10.2307/1970012
[16] G. F. Paechter, The groups \?\?(\?_{\?,\?}). I, Quart. J. Math. Oxford Ser. (2) 7 (1956), 249 – 268. · Zbl 0073.18402 · doi:10.1093/qmath/7.1.249
[17] Anthony Phillips, Submersions of open manifolds, Topology 6 (1967), 171 – 206. · Zbl 0204.23701 · doi:10.1016/0040-9383(67)90034-1
[18] Norman Steenrod, The Topology of Fibre Bundles, Princeton Mathematical Series, vol. 14, Princeton University Press, Princeton, N. J., 1951. · Zbl 0054.07103
[19] Emery Thomas, Seminar on fiber spaces, Lectures delivered in 1964 in Berkeley and 1965 in Zürich. Berkeley notes by J. F. McClendon. Lecture Notes in Mathematics, vol. 13, Springer-Verlag, Berlin-New York, 1966. · Zbl 0151.31604
[20] Emery Thomas, Postnikov invariants and higher order cohomology operations, Ann. of Math. (2) 85 (1967), 184 – 217. · Zbl 0152.22002 · doi:10.2307/1970439
[21] Emery Thomas, Real and complex vector fields on manifolds, J. Math. Mech. 16 (1967), 1183 – 1205. · Zbl 0153.53503
[22] Emery Thomas, Submersions and immersions with codimension one or two, Proc. Amer. Math. Soc. 19 (1968), 859 – 863. · Zbl 0169.26102
[23] Hassler Whitney, Differentiable manifolds, Ann. of Math. (2) 37 (1936), no. 3, 645 – 680. · Zbl 0015.32001 · doi:10.2307/1968482
[24] W. Wu, Classes caractéristique et i-carrés d’une variété, C. R. Acad. Sci. Paris 230 (1950), 508-521. · Zbl 0035.11002
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