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Compact Lie group actions and fiber homotopy type
Katsuo KAWAKUBO
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Katsuo KAWAKUBO
Department of Mathematics Faculty of Science Osaka University
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1981 Volume 33 Issue 2 Pages 295-321
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- Published: 1981 Received: December 16, 1978 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. F. Adams, On the group J(X)-I, Topology, 2 (1963), 181-195.
2) M. F. Atiyah, Thom complexes, Proc. London Math. Soc., (3) 11 (1961), 291-310.
3) M. F. Atiyah and G. B. Segal, Equivariant K-theory, (mimeographed note), University of Warwick.
4) W. Browder, Homotopy type of differentiable manifolds, Proceedings of the Aarhus Symposium on Algebraic Topology, Aarhus, (1962), 42-46.
5) T. tom Dieck, Characteristic numbers of G-manifolds, I, Invent. Math., 13 (1971), 213-224.
6) T. tom Dieck, Oberwolfach talk, 1976, September.
7) A. Dold, Über fasernweise Homotopieäquivalenz von Faserräumen, Math. Z., 62 (1955), 111-136.
8) M. W. Hirsch, On the fiber homotopy type of normal bundles, Michigan Math. J., 12 (1965), 225-229.
9) W. C. Hsiang, A note on free differentiable actions of S1 and S3 on homotopy spheres, Ann. of Math., 83 (1966), 266-272.
10) S. Illman, Equivariant singular homology and cohomology for actions of compact Lie groups, Proc. of the Second Conf. on Compact Transformation Groups, Amherst, Springer Lecture Note, 298 (1971), 403-415.
11) K. Jänich, On the classification of O(n) manifolds, Math. Ann., 176 (1968), 53-76.
12) K. Kawakubo, Free and semi-free differentiable actions on homotopy spheres, Proc. Japan Acad., 45 (1969), 651-655.
13) K. Kawakubo, Equivariant Riemann-Rock theorems, localization and formal group law, (mimeographed note), Universität Bonn, 1976.
14) M. A. Kervaire, S. Maumary and G. de Rham, Torsion et type simple d'homotopie, Springer Lecture Note, 48 (1967).
15) J. L. Koszul, Sur certain groupes de transformation de Lie, Colloque de Geometrie Differentiable, Strasbourg, 1953.
16) T. Matumoto, On G-CW complexes and a theorem of J.H.C. Whitehead, J. Fac. Sci. Univ. Tokyo Sect. IA, 18 (1971), 363-374.
17) J. Milnor, Two complexes which are homeomorphic but combinatorially distinct, Ann. of Math., 74 (1961), 575-590.
18) S. P. Novikov, Homotopy equivalent smooth manifolds, I, Izv. Acad. Nauk SSSR Ser. Mat., 28 (1964), 365-474, A.M.S. Translations, 48 (1965), 271-396.
19) R. Palais, Imbeddings of compact, differentiable transformation groups in orthogonal representations, J. Math. Mech., 6 (1957), 673-678.
20) R. L. Rubinsztein, On the equivariant homotopy of spheres, Dissertationes Mathematicae, Warszawa, 1976.
21) G. Segal, Equivariant stable homotopy theory, Actes, Congrés internat. math. (Nice, 1970), T.2, 59-63, Gauthier-Villars, Paris, 1971.
22) C.T.C. Wall, Surgery on compact manifolds, Academic Press, 1970.
23) A.G. Wasserman, Equivariant differential topology, Topology, 8 (1969), 127-150.
24) J.H.C. Whitehead, Combinatorial homotopy, I, Bull. Amer. Math. Soc., 55 (1949), 213-245.
25) C.T. Yang, The triangulability of the orbit space of a differentiable transformation group, Bull. Amer. Math. Soc., 69 (1963), 405-408.
Right : [1] J. F. Adams, On the group J(X)-I, Topology, 2 (1963), 181-195.
[2] M. F. Atiyah, Thom complexes, Proc. London Math. Soc., (3) 11 (1961), 291-310.
[3] M. F. Atiyah and G. B. Segal, Equivariant K-theory, (mimeographed note), University of Warwick.
[4] W. Browder, Homotopy type of differentiable manifolds, Proceedings of the Aarhus Symposium on Algebraic Topology, Aarhus, (1962), 42-46.
[5] T. tom Dieck, Characteristic numbers of G-manifolds, I, Invent. Math., 13 (1971), 213-224.
[6] T. tom Dieck, Oberwolfach talk, 1976, September.
[7] A. Dold, Über fasernweise Homotopieäquivalenz von Faserräumen, Math. Z., 62 (1955), 111-136.
[8] M. W. Hirsch, On the fiber homotopy type of normal bundles, Michigan Math. J., 12 (1965), 225-229.
[9] W. C. Hsiang, A note on free differentiable actions of S1 and S3 on homotopy spheres, Ann. of Math., 83 (1966), 266-272.
[10] S. Illman, Equivariant singular homology and cohomology for actions of compact Lie groups, Proc. of the Second Conf. on Compact Transformation Groups, Amherst, Springer Lecture Note, 298 (1971), 403-415.
[11] K. Jänich, On the classification of O(n) manifolds, Math. Ann., 176 (1968), 53-76.
[12] K. Kawakubo, Free and semi-free differentiable actions on homotopy spheres, Proc. Japan Acad., 45 (1969), 651-655.
[13] K. Kawakubo, Equivariant Riemann-Roch theorems, localization and formal group law, (mimeographed note), Universität Bonn, 1976.
[14] M. A. Kervaire, S. Maumary and G. de Rham, Torsion et type simple d'homotopie, Springer Lecture Note, 48 (1967).
[15] J. L. Koszul, Sur certain groupes de transformation de Lie, Colloque de Geometrie Differentiable, Strasbourg, 1953.
[16] T. Matumoto, On G-CW complexes and a theorem of J. H. C. Whitehead, J. Fac. Sci. Univ. Tokyo Sect. IA, 18 (1971), 363-374.
[17] J. Milnor, Two complexes which are homeomorphic but combinatorially distinct, Ann. of Math., 74 (1961), 575-590.
[18] S. P. Novikov, Homotopy equivalent smooth manifolds, I, Izv. Acad. Nauk SSSR Ser. Mat., 28 (1964), 365-474, A. M. S. Translations, 48 (1965), 271-396.
[19] R. Palais, Imbeddings of compact, differentiable transformation groups in orthogonal representations, J. Math. Mech., 6 (1957), 673-678.
[20] R. L. Rubinsztein, On the equivariant homotopy of spheres, Dissertationes Mathematicae, Warszawa, 1976.
[21] G. Segal, Equivariant stable homotopy theory, Actes, Congrés internat. math. (Nice, 1970), T. 2, 59-63, Gauthier-Villars, Paris, 1971.
[22] C. T. C. Wall, Surgery on compact manifolds, Academic Press, 1970.
[23] A. G. Wasserman, Equivariant differential topology, Topology, 8 (1969), 127-150.
[24] J. H. C. Whitehead, Combinatorial homotopy, I, Bull. Amer. Math. Soc., 55 (1949), 213-245.
[25] C. T. Yang, The triangulability of the orbit space of a differentiable transformation group, Bull. Amer. Math. Soc., 69 (1963), 405-408.
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