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

Tsutomu YASUI

doi:10.2969/jmsj/03640555

Tsutomu YASUI

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JOURNAL FREE ACCESS

1984 Volume 36 Issue 4 Pages 555-576

DOI https://doi.org/10.2969/jmsj/03640555

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Published: 1984 Received: March 30, 1983 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 Minoru Nakaoka 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), 263-403.
2) A. Dold, Erzeugende der Thomschen Algebra _??_, Math. Z., 65 (1956), 25-35.
3) R. Greenblatt, The twisted Bockstein coboundary, Proc. Cambridge Philos. Soc., 61 (1965), 295-297.
4) A. Haefliger, Points multiples d'une application et produit cyclique réduit, Amer. J. Math., 83 (1961), 57-70.
5) A. Haefliger, Plongements différentiables dans le domaine stable, Comment. Math. Helv., 37 (1962), 155-176.
6) A. Haefliger, Plongement de variétés dans le domaine stable, Séminaire Bourbaki, 150 (1962/63), n° 245.
7) A. Haefliger and M. W. Hirsch, On the existence and classification of differentiable embeddings, Topology, 2 (1962), 129-135.
8) L. L. Larmore, The cohomology of (Λ²X, ΔX), Canad. J. Math., 25 (1973), 908-921.
9) L. L. Larmore and R. D. Rigdon, Enumerating immersions and embeddings of projective spaces, Pacific J. Math., 64 (1976), 471-492.
10) W. S. Massey and F. P. Peterson, On the dual Stiefel-Whitney classes of a manifold, Bol. Mat. Soc. Mexicana, 8 (1963), 1-13.
11) J. W. Milnor and J. D. Stasheff, Characteristic classes, Ann. of Math. Stud., 76, Princeton Univ. Press, 1974.
12) M. Nakaoka, Cohomology theory of a complex with a transformation of prime period and its applications, J. Inst. Polyt., Osaka City Univ., 7 (1965), 51-102.
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) J. Siegel, Higher order cohomology operations in local coefficient theory, Amer. J. Math., 89 (1967), 909-931.
16) E. H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966.
17) E. Thomas, Embedding manifolds in Euclidean space, Osaka J. Math., 13 (1976), 163-186.
18) T. Yasui, The enumeration of liftings in fibrations and the embedding problem I, Hiroshima Math. J., 6 (1976), 227-255.
19) T. Yasui, On the maps defined by regarding embeddings as immersions, to appear in Hiroshima Math. J., 13.
20) T. Yasui, Notes on enumerating embeddings of unorientable n-manifolds in Euclidean (2n-1)-space for odd n, to appear in Bull. of Yamagata Univ., Natur. Sci., 11.
21) G. Yo, Cohomology operations and duality in a manifold, Sci. Sinica, 12 (1963), 1469-1487.
22) G. Yo, Cohomology mod p of deleted cyclic product of a manifold, Sci. Sinica, 12 (1963), 1779-1794.
23) J. J. Ucci, Immersions and embeddings of Dold manifolds, Topology, 4 (1965), 283-293.
24) H. Whitney, Differentiable manifolds, Ann. of Math., 37 (1936), 645-680.
25) Wen-Tsun Wu, On the isotopy of C^r-manifolds of dimension n in Euclidean (2n+1)-space, Science Record (N.S.), 2 (1958), 271-275.

Right : [1] D. R. Bausum, Embeddings and immersions of manifolds in Euclidean space, Trans. Amer. Math. Soc., 213 (1975), 263-403.
[2] A. Dold, Erzeugende der Thomschen Algebra ℜ, Math. Z., 65 (1956), 25-35.
[3] R. Greenblatt, The twisted Bockstein coboundary, Proc. Cambridge Philos. Soc., 61 (1965), 295-297.
[4] A. Haefliger, Points multiples d'une application et produit cyclique réduit, Amer. J. Math., 83 (1961), 57-70.
[5] A. Haefliger, Plongements différentiables dans le domaine stable, Comment. Math. Helv., 37 (1962), 155-176.
[6] A. Haefliger, Plongement de variétés dans le domaine stable, Séminaire Bourbaki, 150 (1962/63), n° 245.
[7] A. Haefliger and M. W. Hirsch, On the existence and classification of differentiable embeddings, Topology, 2 (1962), 129-135.
[8] L. L. Larmore, The cohomology of (Λ²X, ΔX), Canad. J. Math., 25 (1973), 908-921.
[9] L. L. Larmore and R. D. Rigdon, Enumerating immersions and embeddings of projective spaces, Pacific J. Math., 64 (1976), 471-492.
[10] W. S. Massey and F. P. Peterson, On the dual Stiefel-Whitney classes of a manifold, Bol. Mat. Soc. Mexicana, 8 (1963), 1-13.
[11] J. W. Milnor and J. D. Stasheff, Characteristic classes, Ann. of Math. Stud., 76, Princeton Univ. Press, 1974.
[12] M. Nakaoka, Cohomology theory of a complex with a transformation of prime period and its applications, J. Inst. Polyt., Osaka City Univ., 7 (1965), 51-102.
[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] J. Siegel, Higher order cohomology operations in local coefficient theory, Amer. J. Math., 89 (1967), 909-931.
[16] E. H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966.
[17] E. Thomas, Embedding manifolds in Euclidean space, Osaka J. Math., 13 (1976), 163-186.
[18] T. Yasui, The enumeration of liftings in fibrations and the embedding problem I, Hiroshima Math. J., 6 (1976), 227-255.
[19] T. Yasui, On the maps defined by regarding embeddings as immersions, to appear in Hiroshima Math. J., 13.
[20] T. Yasui, Notes on enumerating embeddings of unorientable n-manifolds in Euclidean (2n-1)-space for odd n, to appear in Bull. of Yamagata Univ., Natur. Sci., 11.
[21] G. Yo, Cohomology operations and duality in a manifold, Sci. Sinica, 12 (1963), 1469-1487.
[22] G. Yo, Cohomology mod p of deleted cyclic product of a manifold, Sci. Sinica, 12 (1963), 1779-1794.
[23] J. J. Ucci, Immersions and embeddings of Dold manifolds, Topology, 4 (1965), 283-293.
[24] H. Whitney, Differentiable manifolds, Ann. of Math., 37 (1936), 645-680.
[25] Wen-Tsun Wu, On the isotopy of C^r-manifolds of dimension n in Euclidean (2n+1)-space, Science Record (N. S.), 2 (1958), 271-275.

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