Abstract
Biquotients are non-homogeneous quotient spaces of Lie groups. Using the Serre spectral sequence and the method of Borel, we compute the cohomology algebra of these spaces in cases where the Lie group cohomology is not too complicated. Among these are the biquotients which are known to carry a metric of positive curvature.
Similar content being viewed by others
References
S. Aloff & N. L. Wallach:An infinite family of distinct 7-manifolds admitting positively curved Riemannian structures. Bull. Amer. Math. Soc. 81, 93–97 (1975)
A. Borel:Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts. Ann. of Math. 57, 115–207 (1953)
J.-H. Eschenburg:New examples of manifolds with strictly positive curvature. Invent. Math. 66, 469–480 (1982)
J.-H. Eschenburg:Freie isometrische Aktionen auf kompakten Lie-Gruppen mit positiv gekrümmten Orbiträumen. Schr. Math. Inst. Univ. Münster (2) 32 (1984)
J.-H. Eschenburg:Inhomogeneous spaces of positive curvature. To appear in Differential Geometry and its Applications
D. Gromoll & W. T. Meyer:An exotic sphere with non-negative sectional curvature. Ann. of Math. 100, 401–406 (1974)
W. Y. Hsiang:Cohomology Theory of Topological Transformation Groups. Springer 1975
M. Kreck & S. Stolz:Some nondiffeomorphic homeomorphic homogeneous 7-manifolds with positive sectional curvature. J. Differential Geometry 33, 465–486 (1991)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Eschenburg, J.H. Cohomology of biquotients. Manuscripta Math 75, 151–166 (1992). https://doi.org/10.1007/BF02567078
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02567078