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Cheeger manifolds and the classification of biquotients

Burt Totaro
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Abstract

A closed manifold is called a biquotient if it is diffeomorphic to K\G/H for some compact Lie group G with closed subgroups K and H such that K acts freely on G/H. Biquotients are a major source of examples of Riemannian manifolds with nonnegative sectional curvature. We prove several classification results for biquotients: (1) We classify all simply connected rational homology spheres which are diffeomorphic to biquotients. For example, the Gromoll-Meyer exotic sphere is the only exotic sphere of any dimension which is a biquotient. (2) We determine exactly which Cheeger manifolds, the connected sums of two rank-one symmetric spaces, are diffeomorphic to biquotients. For example, CP^2 # CP^2 is a biquotient, but CP^4 # HP^2 is not. (3) There are only finitely many diffeomorphism classes of 2-connected biquotients in each dimension.

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Burt Totaro. 2002-10-16. Cheeger manifolds and the classification of biquotients. https://arxiv.org/abs/math/0210247

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