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Transactions of the American Mathematical Society

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On the existence of immersions and submersions


Author: Emery Thomas
Journal: Trans. Amer. Math. Soc. 132 (1968), 387-394
MSC: Primary 57.20
DOI: https://doi.org/10.1090/S0002-9947-1968-0225332-8
MathSciNet review: 0225332
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  • [1] A. 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. MR 0051508 (14:490e)
  • [2] R. Bott, The stable homotopy of the classical groups, Ann. of Math. (2) 70 (1959), 313-337. MR 0110104 (22:987)
  • [3] W. Browder, J. Levine and G. Livesay, Finding a boundary for an open manifold, Amer. J. Math. 87 (1965), 1017-1028. MR 0189046 (32:6473)
  • [4] S. Feder, Immersions and embeddings in complex projective spaces, Topology 4 (1965), 143-158. MR 0184244 (32:1717)
  • [5] I. M. James and E. Thomas, Submersions and immersions of manifolds, Inventiones Math. 2 (1967), 171-177. MR 0212821 (35:3686)
  • [6] A. Haefliger and M. Hirsch, On the existence and classification of differentiable embeddings, Topology 2 (1963), 129-136. MR 0149494 (26:6981)
  • [7] M. Hirsch, Immersion of manifolds, Trans. Amer. Math. Soc. 93 (1959), 242-276. MR 0119214 (22:9980)
  • [8] -, On imbedding differentiable manifolds in Euclidean space, Ann. of Math. (2) 73 (1961), 566-571. MR 0124915 (23:A2223)
  • [9] S. D. Liao, On the theory of obstructions for fiber bundles, Ann. of Math. (2) 60 (1954), 146-191. MR 0062441 (15:979d)
  • [10] M. Mahowald, On obstruction theory in orientable fiber bundles, Trans. Amer. Math. Soc. 110 (1964), 315-349. MR 0157386 (28:620)
  • [11] M. Mahowald and F. Peterson, Secondary cohomology operations on the Thom class, Topology 2 (1964), 367-377. MR 0157378 (28:612)
  • [12] W. Massey, On the Stiefel-Whitney classes of a manifold, Amer. J. Math. 82 (1960), 92-102. MR 0111053 (22:1918)
  • [13] -, On the Stiefel-Whitney classes of a manifold. II, Proc. Amer. Math. Soc. 13 (1962), 938-942. MR 0142129 (25:5522)
  • [14] W. Massey and F. Peterson, On the dual Stiefel-Whitney classes of a manifold, Bol. Soc. Mat. Mexicana (2) 8 (1963), 1-13. MR 0163325 (29:628)
  • [15] J. Milnor, Construction of universal bundles. II, Ann. of Math. (2) 63 (1956), 430-436. MR 0077932 (17:1120a)
  • [16] G. Paechter, The groups $ {\pi _r}({V_{n,m}})$. I, Quart. J. Math. Oxford Ser. (2) 7 (1956), 249-268. MR 0131878 (24:A1725)
  • [17] A. Phillips, Submersions of open manifolds, Topology 6 (1967), 171-206. MR 0208611 (34:8420)
  • [18] N. Steenrod, The topology of fiber bundles, Princeton Univ. Press, Princeton, N. J., 1951. MR 0039258 (12:522b)
  • [19] E. Thomas, Seminar on fiber spaces, Lecture Notes in Math. No. 13, Springer-Verlag, Heidelberg, 1966. MR 0203733 (34:3582)
  • [20] -, Postnikov invariants and higher order cohomology operations, Ann. of Math. (2) 85 (1967), 184-217. MR 0210135 (35:1029)
  • [21] -, Real and complex vector fields on manifolds, J. Math. Mech. 16 (1967), 1183-1206. MR 0210136 (35:1030)
  • [22] -, Submersions and immersions with codimension one or two, Proc. Amer. Math. Soc. (to appear). MR 0229246 (37:4820)
  • [23] H. Whitney, Differentiable manifolds, Ann. of Math. (2) 37 (1936), 645-680. MR 1503303
  • [24] W. Wu, Classes caractéristique et i-carrés d'une variété, C. R. Acad. Sci. Paris 230 (1950), 508-521.

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DOI: https://doi.org/10.1090/S0002-9947-1968-0225332-8
Article copyright: © Copyright 1968 American Mathematical Society

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