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We give a lower bound for the bottom of the differential form spectrum on hyperbolic manifolds, generalizing thus a well-known result due to Sullivan and Corlette in the function case. Our method is based on the study of the resolvent associated with the Hodge-de Rham laplacian and leads to applications for the (co)homology and topology of certain classes of hyperbolic manifolds.
Carron, Gilles 1 ; Pedon, Emmanuel 2
@article{ASNSP_2004_5_3_4_705_0,
author = {Carron, Gilles and Pedon, Emmanuel},
title = {On the differential form spectrum of hyperbolic manifolds},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {705--747},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 3},
number = {4},
year = {2004},
mrnumber = {2124586},
zbl = {1170.53309},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2004_5_3_4_705_0/}
}
TY - JOUR AU - Carron, Gilles AU - Pedon, Emmanuel TI - On the differential form spectrum of hyperbolic manifolds JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2004 SP - 705 EP - 747 VL - 3 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://geodesic.mathdoc.fr/item/ASNSP_2004_5_3_4_705_0/ LA - en ID - ASNSP_2004_5_3_4_705_0 ER -
%0 Journal Article %A Carron, Gilles %A Pedon, Emmanuel %T On the differential form spectrum of hyperbolic manifolds %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2004 %P 705-747 %V 3 %N 4 %I Scuola Normale Superiore, Pisa %U http://geodesic.mathdoc.fr/item/ASNSP_2004_5_3_4_705_0/ %G en %F ASNSP_2004_5_3_4_705_0
Carron, Gilles; Pedon, Emmanuel. On the differential form spectrum of hyperbolic manifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 3 (2004) no. 4, pp. 705-747. http://geodesic.mathdoc.fr/item/ASNSP_2004_5_3_4_705_0/