A remark on the Ochanine genus

Kaoru ONO

doi:10.2969/jmsj/04440613

Kaoru ONO

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JOURNAL FREE ACCESS

1992 Volume 44 Issue 4 Pages 613-618

DOI https://doi.org/10.2969/jmsj/04440613

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Published: 1992 Received: September 25, 1991 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) M. F. Atiyah and I. M. Singer, Index theory for skew adjoint Fredholm operators, Publ. Math. IHES, 37 (1969), 5-26.
2) M. Bendersky, Application of the Ochanine genus, Math. Z., 206 (1991), 443-455.
3) R. Bott and C. Taubes, On the rigidity theorems of Witten, J. Amer. Math. Soc., 2 (1989), 137-186.
4) A. L. Edmonds, Orientability of fixed point sets, Proc. Amer. Math. Soc., 82 (1981), 120-124.
5) F. Hirzebruch, Mannigfaltigkeiten and Modulformen, Max-Planck-Institut, 91-10, preprint.
6) F. Hirzebruch and P. Slodowy, Elliptic genera, involutions and homogeneous spin manifolds, Geom. Dedicata, 35 (1990), 309-343.
7) N. Hitchin, Harmonic spinors, Adv. in Math., 14 (1974), 1-55.
8) S. Ochanine, Ellptic genera, modular forms over KO^*, and the Brown-Kervaire invariant, Math. Z., 206 (1991), 277-291.
9) S. Ochanine, A vanishing theorem for the elliptic genus, Max-Planck-Institut, 89-78, preprint.
10) S. Ochanine, Signature modulo 16, invariants de Kervaire généralisés et nombres caractéristiques dans la K-théorie réelle, Bull. Soc. Math. France Memoire, 5(1981).
11) K. Ono, α-invariant and S¹ actions, Proc. Amer. Math. Soc., 112 (1991), 597-600.
12) K. Ono, On a theorem of Edmonds, to appear.
13) E. Witten, The index of the Dirac operator in loop space, Elliptic Curves and Modular Forms in Algebraic Topology, (ed. P.S. Landweber), Lecture Notes in Math., 1326, Springer, Berlin-Heidelberg-New York, 1989, pp. 161-181.

Right : [1] M. F. Atiyah and I. M. Singer, Index theory for skew adjoint Fredholm operators, Publ. Math. IHES, 37 (1969), 5-26.
[2] M. Bendersky, Application of the Ochanine genus, Math. Z., 206 (1991), 443-455.
[3] R. Bott and C. Taubes, On the rigidity theorems of Witten, J. Amer. Math. Soc., 2 (1989), 137-186.
[4] A. L. Edmonds, Orientability of fixed point sets, Proc. Amer. Math. Soc., 82 (1981), 120-124.
[5] F. Hirzebruch, Mannigfaltigkeiten and Modulformen, Max-Planck-Institut, 91-10, preprint.
[6] F. Hirzebruch and P. Slodowy, Elliptic genera, involutions and homogeneous spin manifolds, Geom. Dedicata, 35 (1990), 309-343.
[7] N. Hitchin, Harmonic spinors, Adv. in Math., 14 (1974), 1-55.
[8] S. Ochanine, Ellptic genera, modular forms over KO, and the Brown-Kervaire invariant, Math. Z., 206 (1991), 277-291.
[9] S. Ochanine, A vanishing theorem for the elliptic genus, Max-Planck-Institut, 89-78, preprint.
[10] S. Ochanine, Signature modulo 16, invariants de Kervaire généralisés et nombres caractéristiques dans la K-théorie réelle, Bull. Soc. Math. France Memoire, 5(1981).
[11] K. Ono, α-invariant and S¹ actions, Proc. Amer. Math. Soc., 112 (1991), 597-600.
[12] K. Ono, On a theorem of Edmonds, to appear.
[13] E. Witten, The index of the Dirac operator in loop space, Elliptic Curves and Modular Forms in Algebraic Topology, (ed. P. S. Landweber), Lecture Notes in Math., 1326, Springer, Berlin-Heidelberg-New York, 1989, pp. 161-181.

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