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Cohomology of classifying spaces and hermitian representations
Author(s):
George
Lusztig
Journal:
Represent. Theory
1
(1997),
31 - 36.
MSC (1991):
Primary 20G99
Posted:
November 4, 1996
MathSciNet review:
1429373
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Abstract:
It is shown that a large part of the cohomology of the classifying space of a Lie group satisfying certain hypotheses can be obtained by a difference construction from hermitian representations of that Lie group. This result is relevant to the study of Novikov's higher signatures.
References:
- [B]
- A. Borel, Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. Math. 57 (1953), 115-207. MR 14:490e
- [G]
- M. Gromov, Positive curvature, macroscopic dimension, spectral gaps and higher signatures, Functional analysis on the eve of the 21-st century, in honor of I. M. Gelfand, vol. II, Progr. in Math. 132, Birkhäuser, Boston, 1996. CMP 96:12
- [L]
- G. Lusztig, Novikov's higher signature and families of elliptic operators, J. Diff. Geom. 7 (1971), 225-256.
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Additional Information:
George
Lusztig
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email:
gyrui@math.mit.edu
DOI:
10.1090/S1088-4165-97-00004-6
PII:
S 1088-4165(97)00004-6
Received by editor(s):
August 13, 1996
Received by editor(s) in revised form:
August 21, 1996
Posted:
November 4, 1996
Additional Notes:
Supported in part by the National Science Foundation
Copyright of article:
Copyright
1997,
American Mathematical Society
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