Petites valeurs propres et classe d'Euler des S1-fibrés

Annales Scientifiques de l'Ecole Normale Superieure

Volumn 33, Issue 5, 2000, Pages 611-645

  Colbois, Bruno ^a   Courtois, Gilles ^b  

^a UNIVERSITY OF NEUCHÂTEL   (Switzerland)

^b CENTRE DE MATHÉMATIQUES LAURENT SCHWARTZ   (France)

Author keywords

58A07; 58C40; Classe d'Euler; Formes diff rentielles; Valeurs propres

Indexed keywords

EID: 0010354725     PISSN: 00129593     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-9593(00)01048-X     Document Type: Article

References (22)

1. Besse A.L. Einstein Manifolds. Ergebnisse der Math. und ihrer Grenzgebiete Band 10. 1987;Springer-Verlag, Berlin-Heidelberg-New York.
2. Bott R., Tu L.W. Differential Form in Algebraic Topology. Graduate Texts in Mathematics 82. 1982;Springer-Verlag.
3. Chanillo S., Trèves F. On the lowest eigenvalue of the Hodge Laplacian. J. Differential Geom. Vol. 45:(2):1997;273-287.
4. CHEEGER J., FUKAYA K., GROMOV M., Nilpotent structures and invariant metrics on collapsed manifolds, J. Amer. Math. Soc. 5, 327-372.
5. Cheeger J., Gromov M. Collapsing Riemannian manifolds while keeping their curvature bounded I. J. Differential Geom. Vol. 23:1986;309-346.
6. Cheeger J., Gromov M. Collapsing Riemannian manifolds while keeping their curvature bounded I, II. J. Differential Geom. Vol. 32:1990;269-298.
7. Colin de Verdière Y. Sur la multiplicité de la première valeur propre non nulle du Laplacien. Comment. Math. Helv. Vol. 61:1986;254-270.
8. Colbois B., Colin de Verdière Y. Sur la multiplicité d'une surface de Riemann. Comment. Math. Helv. Vol. 63:1988;194-208.
9. Colbois B., Courtois G. A note on the first non-zero eigenvalue of the Laplacian acting on p -forms. Manuscr. Math. Vol. 68:1990;143-160.
10. Courtois G. Spectrum of manifolds with holes. J. Funct. Anal. Vol. 134:(1):1995;194-221.
11. Dai X. Adiabatic limits, non-multiplicativity of signature and Leray spectral sequence. J. Amer. Math. Soc. Vol. 4:(2):1991;265-321.
12. Dodziuk J. Eigenvalues of the Laplacian on forms. Proc. Amer. Math. Soc. Vol. 85:1982;438-443.
13. Forman R. Spectral sequences and adiabatic limits. Comm. Math. Phys. Vol. 168:(1):1995;57-116.
14. Forman R. Hodge theory and spectral sequences. Topology. Vol. 33:(3):1994;591-611.
15. Fukaya K. Collapsing Riemannian manifolds to ones of lower dimension. J. Differential Geom. Vol. 25:1987;139-156.
16. Fukaya K. Collapsing Riemannian manifolds and eigenvalues of the Laplace operator. Invent. Math. Vol. 87:1987;517-547.
17. Gromov M. Paul Levy's isoperimetric inequality. 1980;Institut des Hautes Études Sci, Bures-sur-Yvette, France. Preprint.
18. Gromov M. Curvature diameter and Betti numbers. Comment. Math. Helv. Vol. 56:1981;179-195.
19. Li P. On the Sobolev constant and the p -spectrum of a compact Riemannian manifold. Ann. Sci. Éc. Norm. Sup. Vol. 13:1980;451-469.
20. Li P., Yau S.T. Eigenvalues of a compact Riemannian manifold. Proceedings Symposium on Pure Math. 1980;205-239.
21. Mazzeo R., Melrose R. The adiabatic limit, Hodge cohomology and Leray's spectral sequence for a fibration. J. Differential Geom. Vol. 31:1990;185-213.
22. Warner F.W. Foundations of Differential Manifolds and Lie Groups. 1971;Scott, Foresman and Company Glenview, London.