no. 5
Petites valeurs propres et classe d’Euler des S1- fibrés
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 33 (2000) no. 5, pp. 611-645 
@article{ASENS_2000_4_33_5_611_0,
     author = {Colbois, Bruno and Courtois, Gilles},
     title = {Petites valeurs propres et classe {d{\textquoteright}Euler} des $S1-$ fibr\'es},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {611--645},
     year = {2000},
     publisher = {Elsevier},
     volume = {4e s{\'e}rie, 33},
     number = {5},
     doi = {10.1016/s0012-9593(00)01048-x},
     zbl = {0968.58001},
     language = {fr},
     url = {https://www.numdam.org/articles/10.1016/s0012-9593(00)01048-x/}
}
TY  - JOUR
AU  - Colbois, Bruno
AU  - Courtois, Gilles
TI  - Petites valeurs propres et classe d’Euler des $S1-$ fibrés
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 2000
SP  - 611
EP  - 645
VL  - 33
IS  - 5
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/s0012-9593(00)01048-x/
DO  - 10.1016/s0012-9593(00)01048-x
LA  - fr
ID  - ASENS_2000_4_33_5_611_0
ER  - 
%0 Journal Article
%A Colbois, Bruno
%A Courtois, Gilles
%T Petites valeurs propres et classe d’Euler des $S1-$ fibrés
%J Annales scientifiques de l'École Normale Supérieure
%D 2000
%P 611-645
%V 33
%N 5
%I Elsevier
%U https://www.numdam.org/articles/10.1016/s0012-9593(00)01048-x/
%R 10.1016/s0012-9593(00)01048-x
%G fr
%F ASENS_2000_4_33_5_611_0
Colbois, Bruno; Courtois, Gilles. Petites valeurs propres et classe d’Euler des $S1-$ fibrés. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 33 (2000) no. 5, pp. 611-645. doi: 10.1016/s0012-9593(00)01048-x

[1] Besse A.L., Einstein Manifolds, Ergebnisse der Math. und ihrer Grenzgebiete Band 10, Springer-Verlag, Berlin-Heidelberg-New York, 1987. | Zbl | MR

[2] Bott R., Tu L. W., Differential Form in Algebraic Topology, Graduate Texts in Mathematics 82, Springer-Verlag, 1982. | Zbl | MR

[3] Chanillo S., Trèves F., On the lowest eigenvalue of the Hodge Laplacian, J. Differential Geom. 45 (2) (1997) 273-287. | Zbl | MR

[4] Cheeger J., Fukaya K., Gromov M., Nilpotent structures and invariant metrics on collapsed manifolds, J. Amer. Math. Soc. 5, 327-372. | Zbl | MR

[5] Cheeger J., Gromov M., Collapsing Riemannian manifolds while keeping their curvature bounded I, J. Differential Geom. 23 (1986) 309-346. | Zbl | MR

[6] Cheeger J., Gromov M., Collapsing Riemannian manifolds while keeping their curvature bounded I, II, J. Differential Geom. 32 (1990) 269-298. | Zbl | MR

[7] Colin De Verdière Y., Sur la multiplicité de la première valeur propre non nulle du Laplacien, Comment. Math. Helv. 61 (1986) 254-270. | Zbl | MR

[8] Colbois B., Colin De Verdière Y., Sur la multiplicité d'une surface de Riemann, Comment. Math. Helv. 63 (1988) 194-208. | Zbl | MR

[9] Colbois B., Courtois G., A note on the first non-zero eigenvalue of the Laplacian acting on p-forms, Manuscr. Math. 68 (1990) 143-160. | Zbl | MR

[10] Courtois G., Spectrum of manifolds with holes, J. Funct. Anal. 134 (1) (1995) 194-221. | Zbl | MR

[11] Dai X., Adiabatic limits, non-multiplicativity of signature and Leray spectral sequence, J. Amer. Math. Soc. 4 (2) (1991) 265-321. | Zbl | MR

[12] Dodziuk J., Eigenvalues of the Laplacian on forms, Proc. Amer. Math. Soc. 85 (1982) 438-443. | Zbl | MR

[13] Forman R., Spectral sequences and adiabatic limits, Comm. Math. Phys. 168 (1) (1995) 57-116. | Zbl | MR

[14] Forman R., Hodge theory and spectral sequences, Topology 33 (3) (1994) 591-611. | Zbl | MR

[15] Fukaya K., Collapsing Riemannian manifolds to ones of lower dimension, J. Differential Geom. 25 (1987) 139-156. | Zbl | MR

[16] Fukaya K., Collapsing Riemannian manifolds and eigenvalues of the Laplace operator, Invent. Math. 87 (1987) 517-547. | Zbl | MR

[17] Gromov M., Paul Levy's isoperimetric inequality, Institut des Hautes Études Sci., Bures-sur-Yvette, France, 1980, Preprint.

[18] Gromov M., Curvature diameter and Betti numbers, Comment. Math. Helv. 56 (1981) 179-195. | Zbl | MR

[19] Li P., On the Sobolev constant and the p-spectrum of a compact Riemannian manifold, Ann. Sci. Éc. Norm. Sup. 13 (1980) 451-469. | Zbl | MR | Numdam

[20] Li P., Yau S.T., Eigenvalues of a compact Riemannian manifold, in : Proceedings Symposium on Pure Math., 1980, pp. 205-239. | Zbl | MR

[21] Mazzeo R., Melrose R., The adiabatic limit, Hodge cohomology and Leray's spectral sequence for a fibration, J. Differential Geom. 31 (1990) 185-213. | Zbl | MR

[22] Warner F.W., Foundations of Differential Manifolds and Lie Groups, Scott, Foresman and Company Glenview, London, 1971. | Zbl

Cité par Sources :