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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Characteristic numbers of positively curved spin-manifolds with symmetry


Author: Anand Dessai
Journal: Proc. Amer. Math. Soc. 133 (2005), 3657-3661
MSC (2000): Primary 53C20; Secondary 58J26
Published electronically: June 6, 2005
MathSciNet review: 2163604
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Abstract: Let $M$ be a $Spin$-manifold of positive sectional curvature and dimension $>8$. Suppose a compact connected Lie group $G$ acts smoothly on $M$. We show that the characteristic number $\hat A(M,TM)$ vanishes if $G$contains two commuting involutions acting isometrically on $M$.


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Additional Information

Anand Dessai
Affiliation: Department of Mathematics, University of Münster, D-48149 Münster, Germany
Email: dessai@math.uni-muenster.de

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07928-1
PII: S 0002-9939(05)07928-1
Keywords: Positive curvature, equivariant index theory, elliptic genera
Received by editor(s): October 24, 2003
Received by editor(s) in revised form: July 8, 2004
Published electronically: June 6, 2005
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.