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Embeddings and immersions of manifolds in Euclidean space


Author: David R. Bausum
Journal: Trans. Amer. Math. Soc. 213 (1975), 263-303
MSC: Primary 57D40
DOI: https://doi.org/10.1090/S0002-9947-1975-0474330-1
MathSciNet review: 0474330
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Abstract | References | Similar Articles | Additional Information

Abstract: The problem of computing the number of embeddings or immersions of a manifold in Euclidean space is treated from a different point of view than is usually taken. Also, a theorem dealing with the existence of an embedding of $ {M^m}$ in $ {R^{2m - 2}}$ is given.


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  • [1] D. Bausum, Embeddings and immersions of manifolds in Euclidean space, Ph. D. Thesis, Yale University, New Haven, Conn., 1974. MR 0474330 (57:13976)
  • [2] S. Eilenberg, Homology of spaces with operators. I, Trans. Amer. Math. Soc. 61 (1947), 378-417; errata, ibid. 62 (1947), 548. MR 9, 52. MR 0021313 (9:52b)
  • [3] S. Feder, The reduced symmetric product of projective spaces and the generalized Whitney theorem, Illinois J. Math. 16 (1972), 323-329. MR 45 #6025. MR 0296966 (45:6025)
  • [4] S. Gitler, Immersion and embedding of manifolds, Proc. Sympos. Pure Math., vol. 22, Amer. Math. Soc., Providence, R. I., 1971, pp. 87-96. MR 47 #4275. MR 0315726 (47:4275)
  • [5] R. Greenblatt, The twisted Bockstein coboundary, Proc. Cambridge Philos. Soc. 61 (1965), 295-297. MR 30 #5314. MR 0175129 (30:5314)
  • [6] D. Handel, An embedding theorem for real projective spaces, Topology 7 (1968), 125-130. MR 37 #3582. MR 0227998 (37:3582)
  • [7] A. Haefliger, Points multiples d'une application et produit cyclique réduit, Amer. J. Math. 83 (1961), 57-70. MR 22 #11404. MR 0120655 (22:11404)
  • [8] -, Plongements différentiables dans le domaine stable, Comment. Math. Helv. 37 (1962/63), 155-176. MR 28 #625. MR 0157391 (28:625)
  • [9] A. Haefliger and M. W. Hirsch, Immersions in the stable range, Ann. of Math. (2) 75 (1962), 231-241. MR 26 #784. MR 0143224 (26:784)
  • [10] -, On the existence and classification of differentiable embeddings, Topology 2 (1963), 129-135. MR 26 #6981. MR 0149494 (26:6981)
  • [11] M. W. Hirsch, Immersions of manifolds, Trans. Amer. Math. Soc. 93 (1959), 242-276. MR 22 #9980. MR 0119214 (22:9980)
  • [12] I. M. James and E. Thomas, Note on the classification of cross-sections, Topology 4 (1965), 351-359. MR 35 #3685. MR 0212820 (35:3685)
  • [13] L. L. Larmore and E. Thomas, Groups extensions and twisted cohomology theories, Illinois J. Math. 17 (1973), 397-410. MR 0336744 (49:1517)
  • [14] B. D. Malyĭ, On the Whitney-Mahowald theorem concerning the normal numbers of smooth embeddings, Mat. Zametki 5 (1969), 91-97 = Math. Notes 5 (1969), 57-60. MR 40 #3569. MR 0250330 (40:3569)
  • [15] W. S. Massey, On the Steifel-Whitney classes of a manifold, Amer. J. Math. 82 (1960), 92-102. MR 22 #1918. MR 0111053 (22:1918)
  • [16] W. S. Massey and F. P. Peterson, The cohomology structure of certain fiber spaces. I, Topology 4 (1965), 47-65. MR 32 #6459. MR 0189032 (32:6459)
  • [17] J. F. McClendon, Higher order twisted cohomology operations, Invent. Math. 7 (1969), 183-214. MR 40 #3541. MR 0250302 (40:3541)
  • [18] -, Obstruction theory in fiber spaces, Math. Z. 120 (1971), 1-17. MR 45 #6002. MR 0296943 (45:6002)
  • [19] C. A. Robinson, Moore-Postnikov systems for non-simple fibrations, Illinois J. Math. 16 (1972), 234-242. MR 45 #7714. MR 0298664 (45:7714)
  • [20] -, Stable homotopy theory over a fixed base space, Bull. Amer. Math. Soc. 80 (1974), 248-252. MR 0370586 (51:6813)
  • [21] Emery Thomas, Seminar on fiber spaces, Lecture Notes in Math., vol. 13, Springer-Verlag, Berlin and New York, 1966. MR 34 #3582. MR 0203733 (34:3582)
  • [22] -, Postnikov invariants and higher order cohomology operations, Ann. of Math. (2) 85 (1967), 184-217. MR 35 #1029. MR 0210135 (35:1029)
  • [23] T. Yasui, Corrections to ``The reduced symmetric product of a complex projective space and the embedding problem", Hiroshima Math. J. 2 (1972), 233-237. MR 0353335 (50:5819)
  • [24] -, Note on the embeddings of real projective spaces, Hiroshima Math. J. 3 (1973), 409-418.. MR 0339220 (49:3982)
  • [25] G. Yo (Yueh Ching-chung), Cohomology operations and duality in a manifold, Sci. Sinica 12 (1963), 1469-1487. MR 31 #6227. MR 0182002 (31:6227)
  • [26] -, Coholomogy $ \bmod\;p$ of deleted cyclic product of a manifold, Sci. Sinica 12 (1963), 1779-1794. MR 31 #6228. MR 0182003 (31:6228)
  • [27] -, Cohomology of the projective bundle of a manifold and its application to immersions, Sci. Sinica 14 (1965), 959-963. MR 32 #1723. MR 0184250 (32:1723)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0474330-1
Keywords: Embeddings and immersions, twisted cohomology operations, Postnikov-towers, Bockstein spectral sequence
Article copyright: © Copyright 1975 American Mathematical Society

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