Global and local equivariant characteristic numbers of G-manifolds

Katsuo KAWAKUBO

doi:10.2969/jmsj/03220301

Katsuo KAWAKUBO

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JOURNAL FREE ACCESS

1980 Volume 32 Issue 2 Pages 301-323

DOI https://doi.org/10.2969/jmsj/03220301

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Published: 1980 Received: June 29, 1978 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: CITATION Details: Wrong : 1) J. F. Adams, Lectures on Lie groups, Benjamin, 1969.
2) M. F. Atiyah and G. B. Segal, Equivariant K-theory, Lecture Note, Oxford University, 1965.
3) M. F. Atiyah and G. B. Segal, The index of elliptic operators: II, Ann. of Math., 87 (1968), 531-545.
4) M. F. Atiyah and I. M. Singer, The index of elliptic operators: III, Ann. of Math., 87 (1968), 546-604.
5) A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces I, II, Amer. J. Math., 80 (1958), 458-538; 81 (1959), 315-382.
6) N. Bourbaki, Algèbre commutative, Ch. 2. Localisation, Hermann, Paris, 1961.
7) S. S. Chern, On the characteristic classes of complex sphere bundles and algebraic varieties, Amer. J. Math., 75 (1953), 565-597.
8) P. E. Conner and E. E. Floyd, Differentiable periodic maps, Springer-Verlag, 1964.
9) T. tom Dieck, Localisierung äquivarianter Kohomologie-Theorien, Math. Z., 121 (1971), 253-262.
10) A. Hattori and H. Taniguchi, Smooth S¹-action and bordism, J. Math. Soc. Japan, 24 (1972), 701-731.
11) F. Hirzebruch, Topological methods in algebraic geometry, Third enlarged edition, Springer, Berlin-Heidelberg-New York, 1966.
12) K. Kawakubo, Global and local equivariant characteristic numbers of G-manifolds: I, Topological proof of the G-signature theorem, Osaka University (mimeographed), 1974.
13) K. Kawakubo, Equivariant Riemann-Roch type theorems and related topics, London Mathematical Society Lecture Note Series 26, Cambridge University Press, 1977.
14) K. Kawakubo, Equivariant Riemann-Roch theorems, localization and formal group law, Universität Bonn (mimeographed), 1976.
15) K. Kawakubo and F. Raymond, The index of manifolds with toral actions and geometric interpretations of the σ(∞, (S¹, M)) invariant of Atiyah and Singer, Invent, Math., 15 (1972), 53-66.
16) K. Kawakubo and F. Uchida, On the index of a semi-free S¹-action, J. Math. Soc. Japan, 23 (1971), 351-355.
17) C. Kosniowski and R. E. Stong, Involutions and characteristic numbers, to appear.
18) C. Kosniowski and R. E. Stong, (Z₂)^k-actions and characteristic numbers, to appear.
19) J. Milnor, Characteristic classes, Ann. of Math. Studies, 76, Princeton Univ. Press, 1974.
20) R. Palais, Imbedding of compact, differentiable transformation groups in orthogonal representations, J. Math. Mech., 6 (1957), 673-678.
21) R. Thom, Quelque propriétés globales des variétés différentiables, Comment. Math. Helv., 28 (1954), 17-86.
22) A. Weil, Demonstration topologique d'un théorème fondamental de Cartan, C. R. Acad. Sci., Paris, 200 (1935), 518-520.

Right : [1] J. F. Adams, Lectures on Lie groups, Benjamin, 1969.
[2] M. F. Atiyah and G. B. Segal, Equivariant K-theory, Lecture Note, Oxford University, 1965.
[3] M. F. Atiyah and G. B. Segal, The index of elliptic operators: II, Ann. of Math., 87 (1968), 531-545.
[4] M. F. Atiyah and I. M. Singer, The index of elliptic operators: III, Ann. of Math., 87 (1968), 546-604.
[5] A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces I, II, Amer. J. Math., 80 (1958), 458-538; 81 (1959), 315-382.
[6] N. Bourbaki, Algèbre commutative, Ch. 2. Localisation, Hermann, Paris, 1961.
[7] S. S. Chern, On the characteristic classes of complex sphere bundles and algebraic varieties, Amer. J. Math., 75 (1953), 565-597.
[8] P. E. Conner and E. E. Floyd, Differentiable periodic maps, Springer-Verlag, 1964.
[9] T. tom Dieck, Localisierung äquivarianter Kohomologie-Theorien, Math. Z., 121 (1971), 253-262.
[10] A. Hattori and H. Taniguchi, Smooth S¹-action and bordism, J. Math. Soc. Japan, 24 (1972), 701-731.
[11] F. Hirzebruch, Topological methods in algebraic geometry, Third enlarged edition, Springer, Berlin-Heidelberg-New York, 1966.
[12] K. Kawakubo, Global and local equivariant characteristic numbers of G-manifolds: I, Topological proof of the G-signature theorem, Osaka University (mimeographed), 1974.
[13] K. Kawakubo, Equivariant Riemann-Roch type theorems and related topics, London Mathematical Society Lecture Note Series 26, Cambridge University Press, 1977.
[14] K. Kawakubo, Equivariant Riemann-Roch theorems, localization and formal group law, Universität Bonn (mimeographed), 1976.
[15] K. Kawakubo and F. Raymond, The index of manifolds with toral actions and geometric interpretations of the σ(∞, (S¹, M)) invariant of Atiyah and Singer, Invent, Math., 15 (1972), 53-66.
[16] K. Kawakubo and F. Uchida, On the index of a semi-free S¹-action, J. Math. Soc. Japan, 23 (1971), 351-355.
[17] C. Kosniowski and R. E. Stong, Involutions and characteristic numbers, to appear.
[18] C. Kosniowski and R. E. Stong, (Z₂)^k-actions and characteristic numbers, to appear.
[19] J. Milnor, Characteristic classes, Ann. of Math. Studies, 76, Princeton Univ. Press, 1974.
[20] R. Palais, Imbedding of compact, differentiable transformation groups in orthogonal representations, J. Math. Mech., 6 (1957), 673-678.
[21] R. Thom, Quelque propriétés globales des variétés différentiables, Comment. Math. Helv., 28 (1954), 17-86.
[22] A. Weil, Demonstration topologique d'un théorème fondamental de Cartan, C. R. Acad. Sci., Paris, 200 (1935), 518-520.

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