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Higher dimensional PL knots and knot manifolds
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1969 Volume 21 Issue 3 Pages 458-480
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- Published: 1969 Received: August 23, 1968 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Correction information
Date of correction: September 29, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor Hitoshi Hombu on his sixtieth birthday
Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) W. Browder, Manifolds with π1=Z, Bull. Amer. Math. Soc., 72 (1966), 225-231.
2) W. Browder, Diffeomorphisms of 1-connected manifolds, Trans. Amer. Math. Soc., 128 (1967), 155-163.
3) R. H. Fox and J. W. Milnor, Singularities of 2-spheres in 4-space and cobordism of knots, Osaka J. Math., 3 (1966), 257-267.
4) H. Gluck, The embedding of two spheres in the four sphere, Trans. Amer. Math. Soc., 104 (1964), 303-333.
5) M. W. Hirsch, On combinatorial submanifolds of differentiable manifolds, Comment. Math. Helv., 36 (1961), 103-111.
6) M. W. Hirsch, Obstruction theories for smoothing manifolds and maps, Bull. Amer. Math. Soc., 69 (1963), 352-356.
7) M. W. Hirsch and L. P. Neuwirth, On piecewise regular n-knots, Ann. of Math., 80 (1964), 594-612.
8) J. F. P. Hudson and E. C. Zeeman, On regular neighborhoods, Proc. London Math. Soc., 14 (1964), 719-745.
9) J. F. P. Hudson and D. W. L. Sumners, Knotted ball pairs in unknotted sphere pairs, J. London Math. Soc., 41 (1966), 717-722.
10) M. Kato, Combinatorial prebundles, Part II, Osaka J. Math., 4 (1967), 305-311.
11) M. Kato, A concordance classification of PL homeomorphisms of Sp×Sq, Topology, (to appear).
12) M. Kervaire, Les noeuds de dimensions superieurs, Bull. Soc. Math. France, 93 (1965), 225-271.
13) M. Kervaire, On higher dimensional knots, Proceedings of Symposium in Honor of Marston Morse, Princeton Univ. Press, 1965, 105-119.
14) M. Kervaire and J. W. Milnor, Groups of homotopy spheres, I, Ann. of Math., 77 (1963), 504-537.
15) R. K. Lashof and M. Rothenberg, Microbundles and smoothings, Topology, 3 (1965), 357-388.
16) J. Levine, Unknotting spheres in codimension two, Topology, 3 (1965), 9-16.
17) B. Mazur, On the structure of certain semi-groups of spherical knot classes, Publs. Math. I. H. E. S., 3 (1959), 19-27.
18) J. Munkres, Obstructions to the smoothing of piecewise-differentiable homeomorphisms, Ann. of Math., 72 (1962), 521-554.
19) H. Noguchi, A classification of orientable surfaces in 4-space, Proc. Japan Acad., 39 (1963), 422-423.
20) H. Noguchi, One flat 3-manifolds in 5-space, Osaka J. Math., 1 (1964), 117-125.
21) H. Noguchi, One flat submanifolds with codimension two, Illinois J. Math., 13 (1969), 220-223.
22) H. Noguchi, Obstructions to locally flat embeddings of combinatorial manifolds, Topology, 5 (1966), 203-213.
23) H. Noguchi, Classical combinatorial topology (mimeographed), University of Illinois, 1967.
24) H. Sato, Diffeomorphism groups of Sp×Sq and exotic spheres (to appear).
25) H. Schubert, Die eindeutige Zerlegbarkeit eines Knotens in Primknoten, S. -B. Heidelberger Akad. Wiss. Math. Nat. Kl. 1949, No. 3, 57-104.
26) C. T. C. Wall, Unknotting tori in codimension one and spheres in codimension two, Proc. Camb. Phil. Soc., 61 (1965), 659-664.
27) C. T. C. Wall, Locally flat submanifolds with codimension two, Proc. Camb. Phil. Soc., 63 (1967), 5-8.
28) M. H. A. Newman, Boundaries of ULC sets in euclidean n-space, Proc. Nat. Acad. Sci. U.S.A., 34 (1948) 193-196.
29) E. C. Zeeman, Unknotting combinatorial balls, Ann. of Math., 78 (1962), 501-526.
30) E. C. Zeeman, Seminars on combinatorial topology (mimeographed), Inst. des Hautes Études Sci., Paris (1963-1966).
Right : [1] W. Browder, Manifolds with π1=Z, Bull. Amer. Math. Soc., 72 (1966), 225-231.
[2] W. Browder, Diffeomorphisms of 1-connected manifolds, Trans. Amer. Math. Soc., 128 (1967), 155-163.
[3] R. H. Fox and J. W. Milnor, Singularities of 2-spheres in 4-space and cobordism of knots, Osaka J. Math., 3 (1966), 257-267.
[4] H. Gluck, The embedding of two spheres in the four sphere, Trans. Amer. Math. Soc., 104 (1964), 303-333.
[5] M. W. Hirsch, On combinatorial submanifolds of differentiable manifolds, Comment. Math. Helv., 36 (1961), 103-111.
[6] M. W. Hirsch, Obstruction theories for smoothing manifolds and maps, Bull. Amer. Math. Soc., 69 (1963), 352-356.
[7] M. W. Hirsch and L. P. Neuwirth, On piecewise regular n-knots, Ann. of Math., 80 (1964), 594-612.
[8] J. F. P. Hudson and E. C. Zeeman, On regular neighborhoods, Proc. London Math. Soc., 14 (1964), 719-745.
[9] J. F. P. Hudson and D. W. L. Sumners, Knotted ball pairs in unknotted sphere pairs, J. London Math. Soc., 41 (1966), 717-722.
[10] M. Kato, Combinatorial prebundles, Part II, Osaka J. Math., 4 (1967), 305-311.
[11] M. Kato, A concordance classification of PL homeomorphisms of Sp×Sq, Topology, (to appear).
[12] M. Kervaire, Les noeuds de dimensions superieurs, Bull. Soc. Math. France, 93 (1965), 225-271.
[13] M. Kervaire, On higher dimensional knots, Proceedings of Symposium in Honor of Marston Morse, Princeton Univ. Press, 1965, 105-119.
[14] M. Kervaire and J. W. Milnor, Groups of homotopy spheres, I, Ann. of Math., 77 (1963), 504-537.
[15] R. K. Lashof and M. Rothenberg, Microbundles and smoothings, Topology, 3 (1965), 357-388.
[16] J. Levine, Unknotting spheres in codimension two, Topology, 3 (1965), 9-16.
[17] B. Mazur, On the structure of certain semi-groups of spherical knot classes, Publs. Math. I. H. E. S., 3 (1959), 19-27.
[18] J. Munkres, Obstructions to the smoothing of piecewise-differentiable homeomorphisms, Ann. of Math., 72 (1962), 521-554.
[19] H. Noguchi, A classification of orientable surfaces in 4-space, Proc. Japan Acad., 39 (1963), 422-423.
[20] H. Noguchi, One flat 3-manifolds in 5-space, Osaka J. Math., 1 (1964), 117-125.
[21] H. Noguchi, One flat submanifolds with codimension two, Illinois J. Math., 13 (1969), 220-223.
[22] H. Noguchi, Obstructions to locally flat embeddings of combinatorial manifolds, Topology, 5 (1966), 203-213.
[23] H. Noguchi, Classical combinatorial topology (mimeographed), University of Illinois, 1967.
[24] H. Sato, Diffeomorphism groups of Sp×Sq and exotic spheres (to appear).
[25] H. Schubert, Die eindeutige Zerlegbarkeit eines Knotens in Primknoten, S. -B. Heidelberger Akad. Wiss. Math. Nat. Kl. 1949, No. 3, 57-104.
[26] C. T. C. Wall, Unknotting tori in codimension one and spheres in codimension two, Proc. Camb. Phil. Soc., 61 (1965), 659-664.
[27] C. T. C. Wall, Locally flat submanifolds with codimension two, Proc. Camb. Phil. Soc., 63 (1967), 5-8.
[28] M. H. A. Newman, Boundaries of ULC sets in euclidean n-space, Proc. Nat. Acad. Sci. U. S. A., 34 (1948) 193-196.
[29] E. C. Zeeman, Unknotting combinatorial balls, Ann. of Math., 78 (1962), 501-526.
[30] E. C. Zeeman, Seminars on combinatorial topology (mimeographed), Inst. des Hautes Études Sci., Paris (1963-1966).
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