Differential Geometry
Elliptic genera of level N on complex π2-finite manifolds
Comptes Rendus. Mathématique, Volume 344 (2007) no. 5, pp. 317-320.

We prove the rigidity of the elliptic genera of level N on complex manifolds with finite second homotopy group admitting circle actions, and the vanishing of the Hilbert polynomial of its canonical bundle.

On montre la rigidité des genres elliptiques de niveau N sur les variétés complexes avec deuxième groupe d'homotopie fini et dotées d'actions de S1, et l'annulation du polynôme de Hilbert de son fibré vectoriel canonique.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.01.020
Herrera, Rafael 1

1 Centro de Investigación en Matemáticas, A.P. 402, Guanajuato, Gto., C.P. 36000, Mexico
@article{CRMATH_2007__344_5_317_0,
     author = {Herrera, Rafael},
     title = {Elliptic genera of level {\protect\emph{N}} on complex $ {\pi }_{2}$-finite manifolds},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {317--320},
     publisher = {Elsevier},
     volume = {344},
     number = {5},
     year = {2007},
     doi = {10.1016/j.crma.2007.01.020},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2007.01.020/}
}
TY  - JOUR
AU  - Herrera, Rafael
TI  - Elliptic genera of level N on complex $ {\pi }_{2}$-finite manifolds
JO  - Comptes Rendus. Mathématique
PY  - 2007
SP  - 317
EP  - 320
VL  - 344
IS  - 5
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2007.01.020/
DO  - 10.1016/j.crma.2007.01.020
LA  - en
ID  - CRMATH_2007__344_5_317_0
ER  - 
%0 Journal Article
%A Herrera, Rafael
%T Elliptic genera of level N on complex $ {\pi }_{2}$-finite manifolds
%J Comptes Rendus. Mathématique
%D 2007
%P 317-320
%V 344
%N 5
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2007.01.020/
%R 10.1016/j.crma.2007.01.020
%G en
%F CRMATH_2007__344_5_317_0
Herrera, Rafael. Elliptic genera of level N on complex $ {\pi }_{2}$-finite manifolds. Comptes Rendus. Mathématique, Volume 344 (2007) no. 5, pp. 317-320. doi : 10.1016/j.crma.2007.01.020. http://www.numdam.org/articles/10.1016/j.crma.2007.01.020/

[1] Bott, R.; Taubes, T. On the rigidity theorems of Witten, J. Amer. Math. Soc., Volume 2 (1989) no. 1, pp. 137-186

[2] Bredon, G.E. Representations at fixed points of smooth actions of compact groups, Ann. of Math., Volume 89 (1969) no. 2, pp. 515-532

[3] Herrera, H.; Herrera, R. Aˆ-genus on non-spin manifolds with S1 actions and the classification of positive quaternion-Kähler 12-manifolds, J. Differential Geometry, Volume 61 (2002) no. 3, pp. 341-364

[4] Hirzebruch, F. Elliptic genera of level N for complex manifolds, Como, 1987 (NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.), Volume vol. 250, Kluwer Acad. Publ., Dordrecht (1988), pp. 37-63

[5] Krichever, I.M. Generalized elliptic genera and Baker–Akhiezer functions, Mat. Zametki, Volume 47 (1990) no. 2, pp. 34-45 158 (in Russian); Translation in Math. Notes, 47, 1–2, 1990, pp. 132-142

[6] Ochanine, S. Sur les genres multiplicatifs définis par des intégrales elliptiques, Topology, Volume 26 (1987), pp. 143-151

[7] Taubes, C.H. S1 actions and elliptic genera, Comm. Math. Phys., Volume 122 (1989) no. 3, pp. 455-526

[8] Witten, E. Elliptic genera and quantum field theory, Comm. Math. Phys., Volume 109 (1987), p. 525

[9] Witten, E. The index of the Dirac operator on loop space (Landweber, P.S., ed.), Elliptic Curves and Modular Forms in Algebraic Topology, Lecture Notes in Math., vol. 1326, Springer, Berlin, 1988, pp. 161-181

Cited by Sources: