Enumerating embeddings of homologically (k-1)-connected n-manifolds in Euclidean (2n-k)-space

Tsutomu YASUI

doi:10.2969/jmsj/03810113

Tsutomu YASUI

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JOURNAL FREE ACCESS

1986 Volume 38 Issue 1 Pages 113-126

DOI https://doi.org/10.2969/jmsj/03810113

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Published: 1986 Received: October 01, 1984 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor Nobuo Shimada on his 60th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) D. R. Bausum, Embeddings and immersions of manifolds in Euclidean space, Trans. Amer. Math. Soc., 213 (1975), 263-303.
2) R. Greenblatt, The twisted Bockstein coboundary, Proc. Cambridge Philos. Soc., 61 (1965), 295-297.
3) A. Haefliger, Points multiples d'une application et product cyclique réduit, Amer. J. Math., 83 (1961), 57-70.
4) A. Haefliger, Plongements différentiables dans le domaine stable, Comment. Math. Helv., 37 (1962), 155-176.
5) A. Haefliger, Plongements de variétés Bans le domaine stable, Séminaire Bourbaki, 15 (1962/63), n° 245.
6) A. Haefliger and M. W. Hirsch, On the existence and classification of differentiable embeddings, Topology, 2 (1962), 129-135.
7) A. Haefliger and M. W. Hirsch, Immersions in the stable range, Ann. of Math., 75 (1962), 231-241.
8) I. M. James and E. Thomas, Note on the classification of cross-sections, Topology, 4 (1966), 351-359.
9) L. L. Larmore, The cohomology of (Λ²X, ΔX), Canad. J. Math., 25 (1973), 908-921.
10) J. F. McClendon, Higher order twisted cohomology operations, Invent. Math., 7 (1969), 183-214.
11) J. F. McClendon, Obstruction theory in fiber spaces, Math. Z., 120 (1971), 1-17.
12) J. W. Milnor and J. D. Stasheff, Characteristic classes, Ann. of Math. Studies, 76, Princeton Univ. Press, 1974.
13) R. D. Rigdon, Immersions and embeddings of manifolds in Euclidean space, Thesis, Univ. of California at Berkeley, 1970.
14) H. Samelson, A note on the Bockstein operator, Proc. Amer. Math. Soc., 15 (1964), 450-453.
15) E. H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966.
16) E. Thomas, Embedding manifolds in Euclidean space, Osaka J. Math., 13(1976), 163-186.
17) G. W. Whitehead, Elements of Homotopy Theory, Graduate Texts in Math., 61, Springer-Verlag, New York, 1978.
18) T. Yasui, On the map defined by regarding embeddings as immersions, Hiroshima Math. J., 13 (1983), 457-476.
19) T. Yasui, Enumerating embeddings of n-manifolds in Euclidean (2n-1)-space, J. Math. Soc. Japan, 36 (1984), 555-576.
20) G. Yo, Cohomology operations and duality in a manifold, Sci. Sinica, 12 (1963), 1469-1487.
21) G. Yo, Cohomology mod p of deleted cyclic product of a manifold, Sci. Sinica, 12 (1963), 1779-1794.

Right : [1] D. R. Bausum, Embeddings and immersions of manifolds in Euclidean space, Trans. Amer. Math. Soc., 213 (1975), 263-303.
[2] R. Greenblatt, The twisted Bockstein coboundary, Proc. Cambridge Philos. Soc., 61 (1965), 295-297.
[3] A. Haefliger, Points multiples d'une application et produit cyclique réduit, Amer. J. Math., 83 (1961), 57-70.
[4] A. Haefliger, Plongements différentiables dans le domaine stable, Comment. Math. Helv., 37 (1962), 155-176.
[5] A. Haefliger, Plongements de variétés dans le domaine stable, Séminaire Bourbaki, 15 (1962/63), n° 245.
[6] A. Haefliger and M. W. Hirsch, On the existence and classification of differentiable embeddings, Topology, 2 (1962), 129-135.
[7] A. Haefliger and M. W. Hirsch, Immersions in the stable range, Ann. of Math., 75 (1962), 231-241.
[8] I. M. James and E. Thomas, Note on the classification of cross-sections, Topology, 4 (1966), 351-359.
[9] L. L. Larmore, The cohomology of (Λ²X, ΔX), Canad. J. Math., 25 (1973), 908-921.
[10] J. F. McClendon, Higher order twisted cohomology operations, Invent. Math., 7 (1969), 183-214.
[11] J. F. McClendon, Obstruction theory in fiber spaces, Math. Z., 120 (1971), 1-17.
[12] J. W. Milnor and J. D. Stasheff, Characteristic classes, Ann. of Math. Studies, 76, Princeton Univ. Press, 1974.
[13] R. D. Rigdon, Immersions and embeddings of manifolds in Euclidean space, Thesis, Univ. of California at Berkeley, 1970.
[14] H. Samelson, A note on the Bockstein operator, Proc. Amer. Math. Soc., 15 (1964), 450-453.
[15] E. H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966.
[16] E. Thomas, Embedding manifolds in Euclidean space, Osaka J. Math., 13 (1976), 163-186.
[17] G. W. Whitehead, Elements of Homotopy Theory, Graduate Texts in Math., 61, Springer-Verlag, New York, 1978.
[18] T. Yasui, On the map defined by regarding embeddings as immersions, Hiroshima Math. J., 13 (1983), 457-476.
[19] T. Yasui, Enumerating embeddings of n-manifolds in Euclidean (2n-1)-space, J. Math. Soc. Japan, 36 (1984), 555-576.
[20] G. Yo, Cohomology operations and duality in a manifold, Sci. Sinica, 12 (1963), 1469-1487.
[21] G. Yo, Cohomology mod p of deleted cyclic product of a manifold, Sci. Sinica, 12 (1963), 1779-1794.

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