Petites valeurs propres et classe d’Euler des fibrés
Bruno Colbois; Gilles Courtois
Annales scientifiques de l'École Normale Supérieure (2000)
- Volume: 33, Issue: 5, page 611-645
- ISSN: 0012-9593
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topColbois, Bruno, and Courtois, Gilles. "Petites valeurs propres et classe d’Euler des $S1-$ fibrés." Annales scientifiques de l'École Normale Supérieure 33.5 (2000): 611-645. <http://eudml.org/doc/82529>.
@article{Colbois2000,
author = {Colbois, Bruno, Courtois, Gilles},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {eigenvalue; differential form; Euler class},
language = {fre},
number = {5},
pages = {611-645},
publisher = {Elsevier},
title = {Petites valeurs propres et classe d’Euler des $S1-$ fibrés},
url = {http://eudml.org/doc/82529},
volume = {33},
year = {2000},
}
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
PB - Elsevier
VL - 33
IS - 5
SP - 611
EP - 645
LA - fre
KW - eigenvalue; differential form; Euler class
UR - http://eudml.org/doc/82529
ER -
References
top- [1] BESSE A.L., Einstein Manifolds, Ergebnisse der Math. und ihrer Grenzgebiete Band 10, Springer-Verlag, Berlin-Heidelberg-New York, 1987. Zbl0613.53001MR88f:53087
- [2] BOTT R., TU L. W., Differential Form in Algebraic Topology, Graduate Texts in Mathematics 82, Springer-Verlag, 1982. Zbl0496.55001MR83i:57016
- [3] CHANILLO S., TRÈVES F., On the lowest eigenvalue of the Hodge Laplacian, J. Differential Geom. 45 (2) (1997) 273-287. Zbl0874.58087MR98i:58236
- [4] CHEEGER J., FUKAYA K., GROMOV M., Nilpotent structures and invariant metrics on collapsed manifolds, J. Amer. Math. Soc. 5, 327-372. Zbl0758.53022MR93a:53036
- [5] CHEEGER J., GROMOV M., Collapsing Riemannian manifolds while keeping their curvature bounded I, J. Differential Geom. 23 (1986) 309-346. Zbl0606.53028MR87k:53087
- [6] CHEEGER J., GROMOV M., Collapsing Riemannian manifolds while keeping their curvature bounded I, II, J. Differential Geom. 32 (1990) 269-298. Zbl0727.53043MR92a:53066
- [7] COLIN DE VERDIÈRE Y., Sur la multiplicité de la première valeur propre non nulle du Laplacien, Comment. Math. Helv. 61 (1986) 254-270. Zbl0607.53028MR88b:58140
- [8] COLBOIS B., COLIN DE VERDIÈRE Y., Sur la multiplicité d'une surface de Riemann, Comment. Math. Helv. 63 (1988) 194-208. Zbl0656.53043MR90c:58182
- [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. Zbl0709.53031MR91g:58290
- [10] COURTOIS G., Spectrum of manifolds with holes, J. Funct. Anal. 134 (1) (1995) 194-221. Zbl0847.58076MR97b:58142
- [11] DAI X., Adiabatic limits, non-multiplicativity of signature and Leray spectral sequence, J. Amer. Math. Soc. 4 (2) (1991) 265-321. Zbl0736.58039MR92f:58169
- [12] DODZIUK J., Eigenvalues of the Laplacian on forms, Proc. Amer. Math. Soc. 85 (1982) 438-443. Zbl0502.58038MR84k:58223
- [13] FORMAN R., Spectral sequences and adiabatic limits, Comm. Math. Phys. 168 (1) (1995) 57-116. Zbl0827.58001MR96g:58176
- [14] FORMAN R., Hodge theory and spectral sequences, Topology 33 (3) (1994) 591-611. Zbl0816.55004MR95j:58160
- [15] FUKAYA K., Collapsing Riemannian manifolds to ones of lower dimension, J. Differential Geom. 25 (1987) 139-156. Zbl0606.53027MR88b:53050
- [16] FUKAYA K., Collapsing Riemannian manifolds and eigenvalues of the Laplace operator, Invent. Math. 87 (1987) 517-547. Zbl0589.58034MR88d:58125
- [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. Zbl0467.53021MR82k:53062
- [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. Zbl0466.53023MR82h:58054
- [20] LI P., YAU S.T., Eigenvalues of a compact Riemannian manifold, in : Proceedings Symposium on Pure Math., 1980, pp. 205-239. Zbl0441.58014MR81i:58050
- [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. Zbl0702.58007MR90m:58004
- [22] WARNER F.W., Foundations of Differential Manifolds and Lie Groups, Scott, Foresman and Company Glenview, London, 1971. Zbl0241.58001
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