Characteristic numbers of positively curved spin-manifolds with symmetry

Dessai, Anand

doi:10.1090/S0002-9939-05-07928-1

Characteristic numbers of positively curved spin-manifolds with symmetry
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Proc. Amer. Math. Soc. 133 (2005), 3657-3661 Request permission

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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