Geometrical operations of Whitehead groups

Mitsuyoshi KATO

doi:10.2969/jmsj/02140523

Mitsuyoshi KATO

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JOURNAL FREE ACCESS

1969 Volume 21 Issue 4 Pages 523-542

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

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Published: 1969 Received: February 10, 1969 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: AUTHOR Details: Wrong : Mitsuyoshi KATO¹⁾
Right : Mitsuyoshi KATO¹⁾²⁾

Date of correction: September 29, 2006 Reason for correction: - Correction: AFFILIATION Details: Wrong :
1) Tokyo Metropolitan University and Institute for Advanced Study

Right :
1) Tokyo Metropolitan University
2) Institute for Advanced Study

Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: 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.

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