Volume and bounded cohomology
Publications Mathématiques de l'IHÉS, Volume 56 (1982), pp. 5-99.
@article{PMIHES_1982__56__5_0,
author = {Gromov, Michael},
title = {Volume and bounded cohomology},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {5--99},
publisher = {Institut des Hautes \'Etudes Scientifiques},
volume = {56},
year = {1982},
zbl = {0516.53046},
mrnumber = {84h:53053},
language = {en},
url = {http://www.numdam.org/item/PMIHES_1982__56__5_0/}
}
TY  - JOUR
AU  - Gromov, Michael
TI  - Volume and bounded cohomology
JO  - Publications Mathématiques de l'IHÉS
PY  - 1982
DA  - 1982///
SP  - 5
EP  - 99
VL  - 56
PB  - Institut des Hautes Études Scientifiques
UR  - http://www.numdam.org/item/PMIHES_1982__56__5_0/
UR  - https://zbmath.org/?q=an%3A0516.53046
UR  - https://www.ams.org/mathscinet-getitem?mr=84h:53053
LA  - en
ID  - PMIHES_1982__56__5_0
ER  - 
%0 Journal Article
%A Gromov, Michael
%T Volume and bounded cohomology
%J Publications Mathématiques de l'IHÉS
%D 1982
%P 5-99
%V 56
%I Institut des Hautes Études Scientifiques
%G en
%F PMIHES_1982__56__5_0
Gromov, Michael. Volume and bounded cohomology. Publications Mathématiques de l'IHÉS, Volume 56 (1982), pp. 5-99. http://www.numdam.org/item/PMIHES_1982__56__5_0/

[1] M. Atiyah, Elliptic operators, discrete groups and von Neuman algebras, Astérisque, 32-33 (1976), 43-72. | MR | Zbl

[2] A. Avez, Variétés Riemanniennes sans points focaux, C.R. Acad. Sc. Paris, 270 (1970), 188-191. | MR | Zbl

[3] G. Baumslag, S. Pride, Groups with two more generators than relators, J. Lond. Math. Soc. (2) 17 (1978), 425-426. | MR | Zbl

[4] G. Baumslag, S. Pride, Groups with one more generator than relators, Math. Z., 167 (1979), 279-281. | EuDML | MR | Zbl

[5] R. Bishop, R. Crittenden, Geometry of manifolds, New York, Acad. Press (1964). | MR | Zbl

[6] R. Brooks, Some remarks on bounded cohomology, in Riemannian surfaces and related topics, Ann. Math. Studies, 91 (1981), 53-65. | MR | Zbl

[7] P. Buser, H. Karcher, Gromov's almost flat manifolds, Astérisque, 81 (1981). | MR | Zbl

[8] P. Conner, R. Frank, Actions of compact Lie groups on aspherical manifolds, Topology of Manifolds (Proc. Inst. Univ. Georgia, Athens, GA, 1969), (1970), 227-264. | MR | Zbl

[9] J. Cheeger, Finiteness theorems for Riemannian manifolds, Am. J. Math., 92 (1970), 61-75. | MR | Zbl

[10] J. Cheeger, D. Ebin, Comparison theorems in Riemannian geometry, North Holland, 1975. | MR | Zbl

[11] J. Cheeger, M. Gromov, M. Tailor, Finite propagation Speed, Kernel estimates for functions of the Laplace Operator and the geometry of Complete Riemannian manifold, J. Diff. Geom., 17 (1982), 15-55. | MR | Zbl

[12] E. Dinaburg, On the relations among various entropy characteristics of dynamical systems, Math USSR Izv., 5 (1971), 337-378. | Zbl

[13] P. Eberlein, Lattices in spaces of non-positive curvature, Ann. of Math., 111 (1980), 435-477. | MR | Zbl

[14] H. Furstenberg, Boundary theory and stochastic processes on homogeneous spaces, Proc. Symp. in Pure Math., XXVI (1973), 193-233. | MR | Zbl

[15] S. Gallot, Quantitative Sobolev Estimates on Riemannian manifolds and applications, C.R. Acad. Sc. Paris, 292 (1981), 375-377. | MR | Zbl

[16] S. Gallot, Inégalités de Sobolev et applications géométriques, to appear.

[17] S. Gallot, Inégalités isopérimétriques sur les variétés compactes sans bord, to appear.

[18] D. Gromoll, W. Meyer, W. Klingenberg, Riemannsche Geometrie im Grossen, Springer Lect. Notes, 55 (1978).

[19] F. Greenleaf, Invariant means on topological groups, Van Nostrand, Reinhold Company, 1969. | MR | Zbl

[20] M. Gromov, Manifolds of negative curvature, J. Diff. Geom., 13 (1978), 223-231. | MR | Zbl

[21] M. Gromov, Hyperbolic manifolds, groups and actions, in Riemannian surfaces and related topics, Ann. Math. Studies, 97 (1981), 183-215. | MR | Zbl

[22] M. Gromov, Paul Levy's Isoperimetric inequality, Preprint I.H.E.S., 1980.

[23] M. Gromov, Groups of polynomial growth and expanding maps, Publ. Math. I.H.E.S., 53 (1981), 53-78. | Numdam | MR | Zbl

[24] M. Gromov, Three remarks on geodesic dynamics and the fundamental group, Preprint, SUNY at Stony Brook, 1977. | Zbl

[25] M. Gromov, Hyperbolic manifolds according to Thurston and Jørgensen, Springer Lect. Notes, 842 (1981), 40-53. | Numdam | MR | Zbl

[26] M. Gromov, B. Lawson, Spin and scalar curvature in the presence of a fundamental group, Ann. of Math., 111 (1980), 209-231. | MR | Zbl

[27] U. Haagerup, H. Munkholm, Simplices of maximal volume in Hyperbolic N-space, Preprint, 1979. | Zbl

[28] G. Harder, A Gauss-Bonnet formula for discrete arithmetically defined groups, Ann. Sci. École Normale Sup., 4 (1971), 409-455. | Numdam | MR | Zbl

[29] H. Hess, R. Schrader, D. Uhlenbrock, Kato's inequality and the spectral distribution of Laplacians on compact Riemannian manifold, J. Diff. Geom., 15 (1980), 27-39. | MR | Zbl

[30] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero. I, Ann. of Math., 79 (1964), 102-203. | MR | Zbl

[31] H. Hironaka, Triangulation of algebraic sets, Proc. Symp. Pure Math., XXIX (1975), 165-185. | MR | Zbl

[32] N. Hitchin, Compact four dimensional Einstein manifolds, J. Diff. Geom., 9 (1974), 435-441. | MR | Zbl

[33] J. M. Hirsch, W. Thurston, Foliated bundles, invariant measures and flat manifolds, Ann. of Math., 101 (1975), 369-390. | MR | Zbl

[34] T. Jørgensen, Compact 3-manifolds of constant negative curvature flbering over the circle, Ann. of Math., 106 (1977), 61-72. | Zbl

[35] H. Inoue, K. Yano, The Gromov invariant of negatively curved manifolds, Topology, 21 (1981), 83-89. | MR | Zbl

[36] A. Katok, Entropy and closed geodesics, to appear. | Zbl

[37] A. Manning, Topological entropy for geodesic flows, Ann. of Math., 110 (1979), 567-573. | MR | Zbl

[38] G. Margulis, Applications of ergodic theory to the investigation of manifolds of negative curvature, Funct. Ann. App., 3 (1969), 335-336. | MR | Zbl

[39] J. Milnor, On the existence of a connection with curvature zero, Comm. Math. Helv., 32 (1958), 215-233. | MR | Zbl

[40] J. Moore, Semi simplicial complexes and Postnikov systems, Symp. de Top. Alg. Mexico, 1958, 232-248. | MR | Zbl

[41] M. Raghunathan, Discrete subgroups of Lie groups, Springer, 1972. | MR | Zbl

[42] R. Savage, The space of positive definite matrices and Gromov's invariant, Preprint, Univ. of Utah, 1981. | Zbl

[43] T. Soma, The Gromov invariant for links, Inv. Math., 64 (1981), 445-454. | MR | Zbl

[44] D. Sullivan, A generalization of Milnor's inequality concerning affine foliations and affine manifolds, Comm. Math. Helv., 51 (1976), 183-189. | MR | Zbl

[45] D. Sullivan, Cycles for the dynamical study of foliated manifolds and complex manifolds, Inv. Math., 36 (1976), 225-255. | MR | Zbl

[46] D. Sullivan, On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions, in Riemannian surfaces and related topics, Ann. Math. Studies, 97 (1981), 465-497. | MR | Zbl

[47] W. Thurston, Geometry and topology of 3-manifolds, Lecture Notes, Princeton, 1978.

[48] H. Winkelnkemper, Un teorema sobre variedades de dimension 4, Acta Mexicana Ci. Tecn., 2 (1968), 88-89. | MR | Zbl

[49] K. Yano, Gromov invariant and S1-actions, to appear. | Zbl

[50] W. Browder, W. C. Hsiang, G-actions and the fundamental group, Inv. Math., 65 (1982), 411-424. | MR | Zbl