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G-maps and tangential representations at G-fixed points of G-manifolds
Masaharu MORIMOTO
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Masaharu MORIMOTO
Department of Mathematics College of Liberal Arts and Sciences Okayama University
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1986 Volume 38 Issue 2 Pages 239-259
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- Published: 1986 Received: May 23, 1984 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 Minoru Nakaoka on his sixtieth birthday
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. Alexander, P. Conner and G. Hamrick, Odd order group actions and Witt classification of inner products, Lecture Notes in Math., 625, Springer, 1977.
2) M. Atiyah, Characters and cohomology of finite groups, Publ. Math. I. H. E. S., 9 (1961), 23-64.
3) M. Atiyah and R. Bott, The Lefschetz fixed-point theorem of elliptic complexes: II. Applications, Ann. of Math., 88 (1968), 451-491.
4) M. Atiyah and I. Singer, The index of elliptic operators: III, Ann. of Math., 87 (1968), 546-604.
5) M. Cohen, A course in simple-homotopy theory, Graduate Texts in Math., 10, Springer, Berlin-New York, 1973.
6) T. tom Dieck, Homotopy-equivalent group representations, J. Reine Angew. Math., 298 (1978), 182-195.
7) T. tom Dieck, Transformation groups and representation theory, Lecture Notes in Math., 766, Springer, 1979.
8) T. tom Dieck and T. Petrie, Geometric modules over the Burnside ring, Invent. Math., 47 (1978), 273-287.
9) K. H. Dovermann and T. Petrie, G-surgery II, Mem. Amer. Math. Soc., 260, 1982.
10) K. H. Dovermann and T. Petrie, An introduction theorem for equivariant surgery (G-surgery III), Amer. J. Math., 105 (1983), 1369-1403.
11) (K. H. Dovermann and) T. Petrie, Rational Smith equivalence, Res. Inst. Math. Sci. Kokyuroku, 501, Kyoto Univ., Kyoto, 1983, 74-85.
12) K. H. Dovermann and M. Rothenberg, An equivariant surgery sequence and equivariant diffeomorphism and homeomorphism classification (A survey), Lecture Notes in Math., 788, Springer, 1980, 257-278.
13) K. H. Dovermann and M. Rothenberg, Poincaré duality and generalized Whitehead torsion, preprint.
14) H. Hauschild, Zerspaltung äquivarianter Homotopiemengen, Math. Ann., 230 (1977), 279-292.
15) S. Illman, Smooth equivariant triangulations of G-manifolds for G a finite group, Math. Ann., 233 (1978), 199-220.
16) K. Kawakubo, Equivariant homotopy equivalence of group representations, J. Math. Soc. Japan, 32 (1980), 105-118.
17) K. Kawakubo, Compact Lie group actions and fiber homotopy type, J. Math. Soc Japan, 33 (1981), 295-321.
18) A. Liulevicius, Characters do not lie, London Math. Soc. Lecture Note Series, 26, 1976, 139-146.
19) M. Masuda and T. Petrie, Lectures on transformation groups and Smith equivalence, Contemporary Math., 36, Amer. Math. Soc., 1985, 191-242.
20) M. Masuda and Y.-D. Tsai, Tangential representations of cyclic group actions on homotopy complex projective spaces, Osaka J. Math., 22 (1985), 907-919.
21) J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc., 72 (1966), 358-426.
22) M. Morimoto and K. Iizuka, Extendibility of G-maps to pseudo-equivalences to finite G-CW complexes whose fundamental groups are finite, Osaka J. Math., 21 (1984), 59-69.
23) R. Oliver, Fixed point set of group actions on finite acyclic complexes, Comment. Math. Helv., 50(1975), 155-177.
24) R. Oliver and T. Petrie, G-CW-surgery and K0 (ZG), Math. Z., 179 (1982), 11-42.
25) K. Pawalowski, Group actions with inequivalent representations at fixed points, Aarhus Preprint Series, 1983/84, No. 32, Aarhus Univ., Aarhus.
26) T. Petrie, Pseudoequivalence of G manifolds, Proc. of Symp. in Pure Math., 32 (1978), 169-210.
27) T. Petrie, One fixed point actions on spheres, I, Adv. in Math., 46(1982), 3-14.
28) T. Petrie, Smith equivalences of representations, Math. Proc. Cambridge Philos. Soc., 94 (1983), 61-99.
29) R. Rubinsztein, On the equivariant homotopy of spheres, Dissertations Math. (Rozprawy Mat.), 134 (1976).
30) G. Segal, Equivariant stable homotopy, Actes Congres intern. Math., 2 (1970), 59-63.
31) J. Shaneson, Wall's surgery obstruction groups for Z×G, Ann. of Math., 90(1969), 296-334.
32) N. Steenrod, The topology of fibre bundles, Princeton Univ. Press, Princeton, 1951.
33) C. T. C. Wall, Surgery on compact manifolds, Academic Press, London, 1970.
Right : [1] J. Alexander, P. Conner and G. Hamrick, Odd order group actions and Witt classification of inner products, Lecture Notes in Math., 625, Springer, 1977.
[2] M. Atiyah, Characters and cohomology of finite groups, Publ. Math. I. H. E. S., 9 (1961), 23-64.
[3] M. Atiyah and R. Bott, The Lefschetz fixed-point theorem of elliptic complexes: II. Applications, Ann. of Math., 88 (1968), 451-491.
[4] M. Atiyah and I. Singer, The index of elliptic operators: III, Ann. of Math., 87 (1968), 546-604.
[5] M. Cohen, A course in simple-homotopy theory, Graduate Texts in Math., 10, Springer, Berlin-New York, 1973.
[6] T. tom Dieck, Homotopy-equivalent group representations, J. Reine Angew. Math., 298 (1978), 182-195.
[7] T. tom Dieck, Transformation groups and representation theory, Lecture Notes in Math., 766, Springer, 1979.
[8] T. tom Dieck and T. Petrie, Geometric modules over the Burnside ring, Invent. Math., 47 (1978), 273-287.
[9] K. H. Dovermann and T. Petrie, G-surgery II, Mem. Amer. Math. Soc., 260, 1982.
[10] K. H. Dovermann and T. Petrie, An introduction theorem for equivariant surgery (G-surgery III), Amer. J. Math., 105 (1983), 1369-1403.
[11] (K. H. Dovermann and) T. Petrie, Rational Smith equivalence, Res. Inst. Math. Sci. Kokyuroku, 501, Kyoto Univ., Kyoto, 1983, 74-85.
[12] K. H. Dovermann and M. Rothenberg, An equivariant surgery sequence and equivariant diffeomorphism and homeomorphism classification (A survey), Lecture Notes in Math., 788, Springer, 1980, 257-278.
[13] K. H. Dovermann and M. Rothenberg, Poincaré duality and generalized Whitehead torsion, preprint.
[14] H. Hauschild, Zerspaltung äquivarianter Homotopiemengen, Math. Ann., 230 (1977), 279-292.
[15] S. Illman, Smooth equivariant triangulations of G-manifolds for G a finite group, Math. Ann., 233 (1978), 199-220.
[16] K. Kawakubo, Equivariant homotopy equivalence of group representations, J. Math. Soc. Japan, 32 (1980), 105-118.
[17] K. Kawakubo, Compact Lie group actions and fiber homotopy type, J. Math. Soc Japan, 33 (1981), 295-321.
[18] A. Liulevicius, Characters do not lie, London Math. Soc. Lecture Note Series, 26, 1976, 139-146.
[19] M. Masuda and T. Petrie, Lectures on transformation groups and Smith equivalence, Contemporary Math., 36, Amer. Math. Soc., 1985, 191-242.
[20] M. Masuda and Y. -D. Tsai, Tangential representations of cyclic group actions on homotopy complex projective spaces, Osaka J. Math., 22 (1985), 907-919.
[21] J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc., 72 (1966), 358-426.
[22] M. Morimoto and K. Iizuka, Extendibility of G-maps to pseudo-equivalences to finite G-CW complexes whose fundamental groups are finite, Osaka J. Math., 21 (1984), 59-69.
[23] R. Oliver, Fixed point set of group actions on finite acyclic complexes, Comment. Math. Helv., 50 (1975), 155-177.
[24] R. Oliver and T. Petrie, G-CW-surgery and K0 (ZG), Math. Z., 179 (1982), 11-42.
[25] K. Pawalowski, Group actions with inequivalent representations at fixed points, Aarhus Preprint Series, 1983/84, No. 32, Aarhus Univ., Aarhus.
[26] T. Petrie, Pseudoequivalence of G manifolds, Proc. of Symp. in Pure Math., 32 (1978), 169-210.
[27] T. Petrie, One fixed point actions on spheres, I, Adv. in Math., 46 (1982), 3-14.
[28] T. Petrie, Smith equivalences of representations, Math. Proc. Cambridge Philos. Soc., 94 (1983), 61-99.
[29] R. Rubinsztein, On the equivariant homotopy of spheres, Dissertations Math. (Rozprawy Mat.), 134 (1976).
[30] G. Segal, Equivariant stable homotopy, Actes Congrès intern. Math., 2 (1970), 59-63.
[31] J. Shaneson, Wall's surgery obstruction groups for Z×G, Ann. of Math., 90 (1969), 296-334.
[32] N. Steenrod, The topology of fibre bundles, Princeton Univ. Press, Princeton, 1951.
[33] C. T. C. Wall, Surgery on compact manifolds, Academic Press, London, 1970.
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