Differential Geometry
Spinc-manifolds and elliptic genera
[Variétés Spinc et genre elliptique]
Comptes Rendus. Mathématique, Tome 336 (2003) no. 12, pp. 1011-1014.

Nous présentons une extension de formules d'annulation d'Alvarez-Gaumé, Witten et Liu lorsqu'on tensorise les fibrés considérés par un fibré en droites complexe. On discute le lien entre nos formules et les formules de congruence d'Ochanine pour les variétés Spinc de dimension 8k+4.

We present an extension of the “miraculous cancellation” formulas of Alvarez-Gaumé, Witten and Kefeng Liu to a twisted version where an extra complex line bundle is involved. Relations to the Ochanine congruence formula on 8k+4 dimensional Spinc manifolds are discussed.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00241-3
Han, Fei 1 ; Zhang, Weiping 1

1 Nankai Institute of Mathematics, Nankai University, Tianjin 300071, PR China
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Han, Fei; Zhang, Weiping. Spinc-manifolds and elliptic genera. Comptes Rendus. Mathématique, Tome 336 (2003) no. 12, pp. 1011-1014. doi : 10.1016/S1631-073X(03)00241-3. http://www.numdam.org/articles/10.1016/S1631-073X(03)00241-3/

[1] Alvarez-Gaumé, L.; Witten, E. Gravitational anomalies, Nucl. Phys. B, Volume 234 (1983), pp. 269-330

[2] Atiyah, M.F.; Hirzebruch, F. Riemann–Roch theorems for differentiable manifolds, Bull. Amer. Math. Soc., Volume 65 (1959), pp. 276-281

[3] Chandrasekharan, K. Elliptic Functions, Springer-Verlag, 1985

[4] Han, F.; Zhang, W. Modular invariance, characteristic numbers and η invariants, Preprint | arXiv

[5] Liu, K. Modular invariance and characteristic numbers, Comm. Math. Phys., Volume 174 (1995), pp. 29-42

[6] Liu, K.; Zhang, W. Elliptic genus and η-invariants, Internat. Math. Res. Notices, Volume 8 (1994), pp. 319-328

[7] Ochanine, S. Signature modulo 16, invariants de Kervaire géneralisé et nombre caractéristiques dans la K-théorie reelle, Mém. Soc. Math. France, Volume 109 (1987), pp. 1-141

[8] Zhang, W. Spinc-manifolds and Rokhlin congruences, C. R. Acad. Sci. Paris, Ser. I, Volume 317 (1993), pp. 689-692

[9] Zhang, W. Lectures on Chern–Weil Theory and Witten Deformations, Nankai Tracks in Math., 4, World Scientific, Singapore, 2001

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