Geometrical operations of Whitehead groups

Mitsuyoshi KATO

doi:10.2969/jmsj/02140523

Mitsuyoshi KATO

著者情報

ジャーナルフリー

1969 年 21 巻 4 号 p. 523-542

DOI https://doi.org/10.2969/jmsj/02140523

詳細

Published: 1969 Received: 1969/02/10 Available on J-STAGE: 2006/09/29 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/09/29 訂正理由: - 訂正箇所: 著者情報訂正内容: Wrong : Mitsuyoshi KATO¹⁾
Right : Mitsuyoshi KATO¹⁾²⁾

訂正日: 2006/09/29 訂正理由: - 訂正箇所: 所属機関情報訂正内容: 訂正前 :
1) Tokyo Metropolitan University and Institute for Advanced Study

訂正後 :
1) Tokyo Metropolitan University
2) Institute for Advanced Study

訂正日: 2006/09/29 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) R.H. Bing and J.M. Kister, Taming complexes in hyperplanes, Duke Math. J., 31 (1964), 491-511.
2) W. Browder, J. Levine and G.R. Livesay, Finding a boundary for an open manifold, Amer. J. Math., 87 (1965), 1017-1028.
3) V.K.A.M. Gugenheim, Piecewise linear isotopy and embedding of elements and spheres I, Proc. London Math. Soc., 3 (1953), 29-53.
4) M.W. Hirsch, On combinatorial submanifolds of differentiable manifolds, Comment. Math. Helv., 36 (1961), 103-111.
5) M.W. Hirsch, Smooth regular neighborhoods, Ann. of Math., 76 (1962), 524-530.
6) J.F.P. Hudson and E.C. Zeeman, On regular neighborhoods, Proc. London Math. Soc., 14 (1964), 719-745.
7) L.S. Hush, Thesis, Florida State University.
8) M. Kato, Regular neighborhoods are not topologically invariant, Bull. Amer. Math. Soc., 74 (1968), 988-991.
9) M. Kato, Higher dimensional PL knots and knot manifolds, J. Math. Soc. Japan, 21 (1969), 458-480.
10) M. Kervaire, Le théorème de Barden-Mazur-Stallings, Comment. Math. Helv., 40 (1965), 31-42.
11) B. Mazur, Differential topology from the point of view of simple homotopy theory, Publ. Math. IHES No. 15.
12) B. Mazur, Corrections to: Differential topology from the point of view of simple homotopy theory, Publ. Math. IHES No. 23.
13) B. Mazur, Relative neighborhoods and the theorems of Smale, Ann. of Math., 77 (1963), 232-249.
14) J. Milnor, Two complexes which are homeomorphic but combinatorially distinct, Ann. of Math., 74 (1961), 575-590.
15) J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc., 72 (1966), 358-426.
16) L.C. Siebenmann and J. Sondow, Some homeomorphic sphere pairs that are combinatorially distinct, Comment. Math. Helv., 41 (1966-67), 261-272.
17) L.C. Siebenmann, On the homotopy type of compact topological manifolds, Bull. Amer. Math. Soc., 74 (1968), 738-742.
18) J. Stallings, On infinite processes leading to differentiability in the complement of a point, Differential and Combinatorial Topology, Princeton Univ. Press, Princeton, N.J., U.S.A., (1965), 245-254.
19) J.H.C. Whitehead, Simple homotopy types, Amer. J. Math., 72 (1950), 1-57.
20) E.C. Zeeman, Seminar on combinatorial topology, IHES (1963), (mimeographed notes).
21) E.C. Zeeman, Twisting spun knots, Trans. Amer. Math. Soc., (3) 115 (1965). 471-495.

Right : [1] R. H. Bing and J.M. Kister, Taming complexes in hyperplanes, Duke Math. J., 31 (1964), 491-511.
[2] W. Browder, J. Levine and G. R. Livesay, Finding a boundary for an open manifold, Amer. J. Math., 87 (1965), 1017-1028.
[3] V. K. A. M. Gugenheim, Piecewise linear isotopy and embedding of elements and spheres I, Proc. London Math. Soc., 3 (1953), 29-53.
[4] M. W. Hirsch, On combinatorial submanifolds of differentiable manifolds, Comment. Math. Helv., 36 (1961), 103-111.
[5] M. W. Hirsch, Smooth regular neighborhoods, Ann. of Math., 76 (1962), 524-530.
[6] J. F. P. Hudson and E. C. Zeeman, On regular neighborhoods, Proc. London Math. Soc., 14 (1964), 719-745.
[7] L. S. Hush, Thesis, Florida State University.
[8] M. Kato, Regular neighborhoods are not topologically invariant, Bull. Amer. Math. Soc., 74 (1968), 988-991.
[9] M. Kato, Higher dimensional PL knots and knot manifolds, J. Math. Soc. Japan, 21 (1969), 458-480.
[10] M. Kervaire, Le théorème de Barden-Mazur-Stallings, Comment. Math. Helv., 40 (1965), 31-42.
[11] B. Mazur, Differential topology from the point of view of simple homotopy theory, Publ. Math. IHES No. 15.
[12] B. Mazur, Corrections to: Differential topology from the point of view of simple homotopy theory, Publ. Math. IHES No. 23.
[13] B. Mazur, Relative neighborhoods and the theorems of Smale, Ann. of Math., 77 (1963), 232-249.
[14] J. Milnor, Two complexes which are homeomorphic but combinatorially distinct, Ann. of Math., 74 (1961), 575-590.
[15] J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc., 72 (1966), 358-426.
[16] L. C. Siebenmann and J. Sondow, Some homeomorphic sphere pairs that are combinatorially distinct, Comment. Math. Helv., 41 (1966-67), 261-272.
[17] L. C. Siebenmann, On the homotopy type of compact topological manifolds, Bull. Amer. Math. Soc., 74 (1968), 738-742.
[18] J. Stallings, On infinite processes leading to differentiability in the complement of a point, Differential and Combinatorial Topology, Princeton Univ. Press, Princeton, N. J., U. S. A., (1965), 245-254.
[19] J. H. C. Whitehead, Simple homotopy types, Amer. J. Math., 72 (1950), 1-57.
[20] E. C. Zeeman, Seminar on combinatorial topology, IHES (1963), (mimeographed notes).
[21] E. C. Zeeman, Twisting spun knots, Trans. Amer. Math. Soc., (3) 115 (1965). 471-495.

訂正日: 2006/09/29 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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