Duke Mathematical Journal

Une suite exacte en $L^2$-cohomologie

Gilles Carron
Source: Duke Math. J. Volume 95, Number 2 (1998), 343-372.
First Page: Show Hide
Primary Subjects: 58G05
Secondary Subjects: 53C21, 58A14
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077229700
Mathematical Reviews number (MathSciNet): MR1652017
Zentralblatt MATH identifier: 0951.58024
Digital Object Identifier: doi:10.1215/S0012-7094-98-09510-2

References

[A] A. Ancona, Théorie du potentiel sur les graphes et les variétés, École d'été de Probabilités de Saint-Flour XVIII, 1988, Lecture Notes in Math., vol. 1427, Springer-Verlag, Berlin, 1990, pp. 1–112.
Mathematical Reviews (MathSciNet): MR92g:31012
Zentralblatt MATH: 0719.60074
[At] M. F. Atiyah, Elliptic operators, discrete groups and von Neumann algebras, Colloque “Analyse et Topologie” en l'Honneur de Henri Cartan (Orsay, 1974), Astérisque, vol. 32-33, Soc. Math. France, Paris, 1976, pp. 43–72.
Mathematical Reviews (MathSciNet): MR54:8741
Zentralblatt MATH: 0323.58015
[APS] M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry, I, Math. Proc. Cambridge Philos. Soc. 77 (1975), 43–69.
Mathematical Reviews (MathSciNet): MR53:1655a
Zentralblatt MATH: 0297.58008
Digital Object Identifier: doi:10.1017/S0305004100049410
[BMS] N. V. Borisov, W. Müller, and R. Schrader, Relative index theorems and supersymmetric scattering theory, Comm. Math. Phys. 114 (1988), no. 3, 475–513.
Mathematical Reviews (MathSciNet): MR89j:58131
Zentralblatt MATH: 0663.58032
Digital Object Identifier: doi:10.1007/BF01242140
Project Euclid: euclid.cmp/1104160691
[B] J. Brüning, $L^2$-index theorems on certain complete manifolds, J. Differential Geom. 32 (1990), no. 2, 491–532.
Mathematical Reviews (MathSciNet): MR91h:58103
Zentralblatt MATH: 0722.58043
Project Euclid: euclid.jdg/1214445317
[BL] J. Brüning and M. Lesch, Hilbert complexes, J. Funct. Anal. 108 (1992), no. 1, 88–132.
Mathematical Reviews (MathSciNet): MR93k:58208
Zentralblatt MATH: 0826.46065
Digital Object Identifier: doi:10.1016/0022-1236(92)90147-B
[C] G. Carron, $L^2$-cohomologie et inégalités de Sobolev, prépublication no. 306, l'Institut J. Fourier, 1994.
[CG] J. Cheeger and M. Gromov, Bounds on the von Neumann dimension of $L^2$-cohomology and the Gauss-Bonnet theorem for open manifolds, J. Differential Geom. 21 (1985), no. 1, 1–34.
Mathematical Reviews (MathSciNet): MR87d:58136
Zentralblatt MATH: 0614.53034
Project Euclid: euclid.jdg/1214439461
[Co] P. E. Conner, The Neumann's problem for differential forms on Riemannian manifolds, Mem. Amer. Math. Soc. 1956 (1956), no. 20, 56.
Mathematical Reviews (MathSciNet): MR17,1197e
Zentralblatt MATH: 0070.31404
[CS] T. Coulhon and L. Saloff-Coste, Isopérimétrie pour les groupes et les variétés, Rev. Mat. Iberoamericana 9 (1993), no. 2, 293–314.
Mathematical Reviews (MathSciNet): MR94g:58263
Zentralblatt MATH: 0782.53066
[dR] G. de Rham, Variétés différentiables. Formes, courants, formes harmoniques, Actualités Sci. Ind., no. 1222 = Publ. Inst. Math. Univ. Nancago III, Hermann et Cie, Paris, 1955.
Mathematical Reviews (MathSciNet): MR16,957b
Zentralblatt MATH: 0065.32401
[Do] J. Dodziuk, de Rham-Hodge theory for $L^2$-cohomology of infinite coverings, Topology 16 (1977), no. 2, 157–165.
Mathematical Reviews (MathSciNet): MR56:3898
Zentralblatt MATH: 0348.58001
Digital Object Identifier: doi:10.1016/0040-9383(77)90013-1
[D] H. Donnelly, Essential spectrum and heat kernel, J. Funct. Anal. 75 (1987), no. 2, 362–381.
Mathematical Reviews (MathSciNet): MR89m:58194
Zentralblatt MATH: 0634.58031
Digital Object Identifier: doi:10.1016/0022-1236(87)90101-7
[DS] G. Duff and D. C. Spencer, Harmonic tensors on Riemannian manifolds with boundary, Ann. of Math. (2) 56 (1952), 128–156.
Mathematical Reviews (MathSciNet): MR13,987a
Zentralblatt MATH: 0049.18901
Digital Object Identifier: doi:10.2307/1969771
[ER] K. D. Elworthy and S. Rosenberg, Manifolds with wells of negative curvature, Invent. Math. 103 (1991), no. 3, 471–495.
Mathematical Reviews (MathSciNet): MR92a:53059
Zentralblatt MATH: 0722.53033
Digital Object Identifier: doi:10.1007/BF01239523
[GM] S. Gallot and D. Meyer, Opérateur de courbure et laplacien des formes différentielles d'une variété riemannienne, J. Math. Pures Appl. (9) 54 (1975), no. 3, 259–284.
Mathematical Reviews (MathSciNet): MR56:13128
Zentralblatt MATH: 0316.53036
[Go] C. Godbillon, Eléments de topologie algébrique, Hermann, Paris, 1971.
Mathematical Reviews (MathSciNet): MR46:880
Zentralblatt MATH: 0218.55001
[G] A. A. Grigor'yan, The existence of positive fundamental solutions of the Laplace equation on Riemannian manifolds, Mat. Sb. (N.S.) 128(170) (1985), no. 3, 354–363.
Mathematical Reviews (MathSciNet): MR87d:58140
Zentralblatt MATH: 0596.31004
[GL] M. Gromov and H. B. Lawson, Jr., Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Inst. Hautes Études Sci. Publ. Math. 58 (1983), 83–196.
Mathematical Reviews (MathSciNet): MR85g:58082
Zentralblatt MATH: 0538.53047
Digital Object Identifier: doi:10.1007/BF02953774
[HS] D. Hoffman and J. Spruck, Sobolev and isoperimetric inequalities for Riemannian submanifolds, Comm. Pure Appl. Math. 27 (1974), 715–727.
Mathematical Reviews (MathSciNet): MR51:1676
Zentralblatt MATH: 0295.53025
[L] J. Lott, $L^ 2$-cohomology of geometrically infinite hyperbolic $3$-manifolds, Geom. Funct. Anal. 7 (1997), no. 1, 81–119.
Mathematical Reviews (MathSciNet): MR98a:58148
Zentralblatt MATH: 0873.57014
Digital Object Identifier: doi:10.1007/PL00001617
[LL] J. Lott and W. Lück, $L^2$-topological invariants of $3$-manifolds, Invent. Math. 120 (1995), no. 1, 15–60.
Mathematical Reviews (MathSciNet): MR96e:58150
Zentralblatt MATH: 0876.57050
Digital Object Identifier: doi:10.1007/BF01241121
[Sp] M. Spivak, A Comprehensive Introduction to Differential Geometry, Vol. III, Publish or Perish Inc., Boston, 1975.
Mathematical Reviews (MathSciNet): MR51:8962
Zentralblatt MATH: 0306.53001
[U] K. Uhlenbeck, The Chern classes of Sobolev connections, Comm. Math. Phys. 101 (1985), no. 4, 449–457.
Mathematical Reviews (MathSciNet): MR87f:58028
Zentralblatt MATH: 0586.53018
Digital Object Identifier: doi:10.1007/BF01210739
Project Euclid: euclid.cmp/1104114242
[Va] N. Varopoulos, Hardy-Littlewood theory for semigroups, J. Funct. Anal. 63 (1985), no. 2, 240–260.
Mathematical Reviews (MathSciNet): MR87a:31011
Zentralblatt MATH: 0608.47047
Digital Object Identifier: doi:10.1016/0022-1236(85)90087-4

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