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

Tsutomu YASUI

doi:10.2969/jmsj/03810113

Tsutomu YASUI

著者情報

ジャーナルフリー

1986 年 38 巻 1 号 p. 113-126

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

詳細

Published: 1986 Received: 1984/10/01 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文サブタイトル訂正内容: Wrong : Dedicated to Professor Nobuo Shimada on his 60th birthday

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: 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.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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