Embeddings and immersions of manifolds in Euclidean space

Bausum, David R.

doi:10.1090/S0002-9947-1975-0474330-1

Embeddings and immersions of manifolds in Euclidean space
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by David R. Bausum

Trans. Amer. Math. Soc. 213 (1975), 263-303

DOI: https://doi.org/10.1090/S0002-9947-1975-0474330-1

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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.

References

David R. Bausum, Embeddings and immersions of manifolds in Euclidean space, Trans. Amer. Math. Soc. 213 (1975), 263–303. MR 474330, DOI 10.1090/S0002-9947-1975-0474330-1
Samuel Eilenberg, Homology of spaces with operators. I, Trans. Amer. Math. Soc. 61 (1947), 378–417; errata, 62, 548 (1947). MR 21313, DOI 10.1090/S0002-9947-1947-0021313-4
S. Feder, The reduced symmetric product of projective spaces and the generalized Whitney theorem, Illinois J. Math. 16 (1972), 323–329. MR 296966, DOI 10.1215/ijm/1256052288
S. Gitler, Immersion and embedding of manifolds, Algebraic topology (Proc. Sympos. Pure Math., Vol. XXII, Univ. Wisconsin, Madison, Wis., 1970) Amer. Math. Soc., Providence, R.I., 1971, pp. 87–96. MR 0315726
Robert Greenblatt, The twisted Bockstein coboundary, Proc. Cambridge Philos. Soc. 61 (1965), 295–297. MR 175129, DOI 10.1017/s0305004100038871
David Handel, An embedding theorem for real projective spaces, Topology 7 (1968), 125–130. MR 227998, DOI 10.1016/0040-9383(68)90020-7
André Haefliger, Points multiples d’une application et produit cyclique réduit, Amer. J. Math. 83 (1961), 57–70 (French). MR 120655, DOI 10.2307/2372720
André Haefliger, Plongements différentiables dans le domaine stable, Comment. Math. Helv. 37 (1962/63), 155–176 (French). MR 157391, DOI 10.1007/BF02566970
André Haefliger and Morris W. Hirsch, Immersions in the stable range, Ann. of Math. (2) 75 (1962), 231–241. MR 143224, DOI 10.2307/1970171
André Haefliger and Morris W. Hirsch, On the existence and classification of differentiable embeddings, Topology 2 (1963), 129–135. MR 149494, DOI 10.1016/0040-9383(63)90028-4
Morris W. Hirsch, Immersions of manifolds, Trans. Amer. Math. Soc. 93 (1959), 242–276. MR 119214, DOI 10.1090/S0002-9947-1959-0119214-4
Ioan James and Emery Thomas, Note on the classification of cross-sections, Topology 4 (1966), 351–359. MR 212820, DOI 10.1016/0040-9383(66)90033-4
L. L. Larmore and E. Thomas, Group extensions and twisted cohomology theories, Illinois J. Math. 17 (1973), 397–410. MR 336744, DOI 10.1215/ijm/1256051607
B. D. Malyĭ, On the Whitney-Mahowald theorem concerning the normal numbers of smooth imbeddings, Mat. Zametki 5 (1969), 91–97 (Russian). MR 250330
W. S. Massey, On the Stiefel-Whitney classes of a manifold, Amer. J. Math. 82 (1960), 92–102. MR 111053, DOI 10.2307/2372878
W. S. Massey and F. P. Peterson, The cohomology structure of certain fibre spaces. I, Topology 4 (1965), 47–65. MR 189032, DOI 10.1016/0040-9383(65)90048-0
J. F. McClendon, Higher order twisted cohomology operations, Invent. Math. 7 (1969), 183–214. MR 250302, DOI 10.1007/BF01404305
James F. McClendon, Obstruction theory in fiber spaces, Math. Z. 120 (1971), 1–17. MR 296943, DOI 10.1007/BF01109713
C. A. Robinson, Moore-Postnikov systems for non-simple fibrations, Illinois J. Math. 16 (1972), 234–242. MR 298664, DOI 10.1215/ijm/1256052280
C. A. Robinson, Stable homotopy theory over a fixed base space, Bull. Amer. Math. Soc. 80 (1974), 248–252. MR 370586, DOI 10.1090/S0002-9904-1974-13447-6
Emery Thomas, Seminar on fiber spaces, Lecture Notes in Mathematics, vol. 13, Springer-Verlag, Berlin-New York, 1966. Lectures delivered in 1964 in Berkeley and 1965 in Zürich; Berkeley notes by J. F. McClendon. MR 0203733, DOI 10.1007/BFb0097864
Emery Thomas, Postnikov invariants and higher order cohomology operations, Ann. of Math. (2) 85 (1967), 184–217. MR 210135, DOI 10.2307/1970439
Tsutomu Yasui, Corrections to: “The reduced symmetric product of a complex projective space and the embedding problem” Hiroshima Math. J. 1 (1971), 27–40, Hiroshima Math. J. 2 (1972), 233–237. MR 353335
Tsutomu Yasui, Note on the enumeration of embeddings of real projective spaces, Hiroshima Math. J. 3 (1973), 409–418. MR 339220
Yo Ging-tzung, Cohomology operations and duality in a manifold, Sci. Sinica 12 (1963), 1469–1487. MR 182002
Yo Ging-tzung, Cohomology $\textrm {mod}\ p$ of deleted cyclic product of a manifold, Sci. Sinica 12 (1963), 1779–1794. MR 182003
Yo Ging-tzung, Cohomology of the projective bundle of a manifold and its application to immersions, Sci. Sinica 14 (1965), 959–963. MR 184250