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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

Lifting group actions and nonnegative curvature


Authors: Karsten Grove and Wolfgang Ziller
Journal: Trans. Amer. Math. Soc. 363 (2011), 2865-2890
MSC (2010): Primary 53C29, 53C07
Published electronically: January 7, 2011
MathSciNet review: 2775790
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Abstract | References | Similar Articles | Additional Information

Abstract: We examine the question when a group acting by cohomogeneity one on the base of a principal $ \operatorname{G}$-bundle can be lifted to the total space and commutes with the action by $ \operatorname{G}$. We answer this question completely when the base of the principle bundle is $ 4$-dimensional.


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Additional Information

Karsten Grove
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Address at time of publication: Department of Mathematics, University of Notre Dame, 255 Hurley Hall, Notre Dame, Indiana 46556-4618
Email: kng@math.umd.edu, kgrove2@nd.edu

Wolfgang Ziller
Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104
Email: wziller@math.upenn.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05272-4
Received by editor(s): November 15, 2008
Published electronically: January 7, 2011
Additional Notes: The first author was supported in part by the Danish Research Council
The second author was supported by the Francis J. Carey Term Chair and the Clay Institute. Both authors were supported by grants from the National Science Foundation.
Article copyright: © Copyright 2011 American Mathematical Society