Equivariant s-cobordism theorems

Shôrô ARAKI; Katsuo KAWAKUBO

doi:10.2969/jmsj/04020349

Shôrô ARAKI, Katsuo KAWAKUBO

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JOURNAL FREE ACCESS

1988 Volume 40 Issue 2 Pages 349-367

DOI https://doi.org/10.2969/jmsj/04020349

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Published: 1988 Received: November 27, 1985 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 Itiro Tamura on his 60th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: AUTHOR Details: Wrong : Shoro ARAKI¹⁾, Katsuo KAWAKUBO²⁾
Right : Shôrô ARAKI¹⁾, Katsuo KAWAKUBO²⁾

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) D. R. Anderson, Torsion invariants and actions of finite groups, Michigan Math. J., 29 (1982), 27-42.
2) S. Araki, Equivariant Whitehead groups and G-expansion categories, to appear.
3) M. M. Cohen, A course in simple homotopy theory, Graduate Texts in Math., 10, Springer, 1973.
4) H. Hauschild, Äquivariante Whiteheadtorsion, Manuscripta Math., 26 (1978), 63-82.
5) M. W. Hirsch, On tangential equivalence of manifolds, Ann. of Math., 83 (1966), 211-217.
6) S. Illman, Whitehead torsion and group actions, Ann. Acad. Sci. Fenn., Ser. AI, 558 (1974), 1-45.
7) S. Illman, Smooth equivariant triangulations of G-manifolds for G a finite group, Math. Ann., 233 (1978), 199-220.
8) S. Illman, Actions of compact Lie groups and the equivariant Whitehead group, preprint, Purdue University, 1983, to appear in Osaka J. Math.
9) S. Illman, Equivariant Whitehead torsion and actions of compact Lie groups, Contemp. Math., 36 (1985), 91-106.
10) I. M. James and G. B. Segal, On equivariant homotopy type, Topology, 17 (1978), 267-272.
11) K. Kawakubo, Compact Lie group actions and fiber homotopy type, J. Math. Soc. Japan, 33 (1981), 295-321.
12) K. Kawakubo, Stable equivalence of G-manifolds, to appear.
13) T. Matumoto and M. Shiota, Unique triangulation of the orbit space of a differentiable transformation group and its applications, to appear.
14) B. Mazur, Stable equivalence of differentiable manifolds, Bull. Amer. Math. Soc., 67 (1961), 377-384.
15) B. Mazur, Relative neighborhoods and the theorem of Smale, Ann. of Math., 77 (1963), 232-249.
16) J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc., 72 (1966), 358-426.
17) M. Rothenberg, Torsion invariants and finite transformation groups, Proc. Symp. in Pure Math., Amer. Math. Soc., 32 (1978), 267-311.
18) M. Steinberger and J. West, Equivariant h-cobordisms and finiteness obstruction, Bull. Amer. Math. Soc., 12 (1985), 217-220.
19) J. B. Wagoner, Diffeomorphisms, K₂, and analytic torsion, Proc. Symp. in Pure Math., Amer. Math. Soc., 32 (1978), 23-33.
20) W. Browder and F. Quinn, A surgery theory for G-manifolds and stratified sets, Manifolds, Univ. of Tokyo Press, Tokyo, 1973.

Right : [1] D. R. Anderson, Torsion invariants and actions of finite groups, Michigan Math. J., 29 (1982), 27-42.
[2] S. Araki, Equivariant Whitehead groups and G-expansion categories, to appear.
[3] M. M. Cohen, A course in simple homotopy theory, Graduate Texts in Math., 10, Springer, 1973.
[4] H. Hauschild, Äquivariante Whiteheadtorsion, Manuscripta Math., 26 (1978), 63-82.
[5] M. W. Hirsch, On tangential equivalence of manifolds, Ann. of Math., 83 (1966), 211-217.
[6] S. Illman, Whitehead torsion and group actions, Ann. Acad. Sci. Fenn., Ser. AI, 558 (1974), 1-45.
[7] S. Illman, Smooth equivariant triangulations of G-manifolds for G a finite group, Math. Ann., 233 (1978), 199-220.
[8] S. Illman, Actions of compact Lie groups and the equivariant Whitehead group, preprint, Purdue University, 1983, to appear in Osaka J. Math.
[9] S. Illman, Equivariant Whitehead torsion and actions of compact Lie groups, Contemp. Math., 36 (1985), 91-106.
[10] I. M. James and G. B. Segal, On equivariant homotopy type, Topology, 17 (1978), 267-272.
[11] K. Kawakubo, Compact Lie group actions and fiber homotopy type, J. Math. Soc. Japan, 33 (1981), 295-321.
[12] K. Kawakubo, Stable equivalence of G-manifolds, to appear.
[13] T. Matumoto and M. Shiota, Unique triangulation of the orbit space of a differentiable transformation group and its applications, to appear.
[14] B. Mazur, Stable equivalence of differentiable manifolds, Bull. Amer. Math. Soc., 67 (1961), 377-384.
[15] B. Mazur, Relative neighborhoods and the theorem of Smale, Ann. of Math., 77 (1963), 232-249.
[16] J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc., 72 (1966), 358-426.
[17] M. Rothenberg, Torsion invariants and finite transformation groups, Proc. Symp. in Pure Math., Amer. Math. Soc., 32 (1978), 267-311.
[18] M. Steinberger and J. West, Equivariant h-cobordisms and finiteness obstruction, Bull. Amer. Math. Soc., 12 (1985), 217-220.
[19] J. B. Wagoner, Diffeomorphisms, K₂, and analytic torsion, Proc. Symp. in Pure Math., Amer. Math. Soc., 32 (1978), 23-33.
[20] W. Browder and F. Quinn, A surgery theory for G-manifolds and stratified sets, Manifolds, Univ. of Tokyo Press, Tokyo, 1973.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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