2002/10/16 by Burt Totaro, Totaro, Burt
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.AT #math.DG #msc:53C20 #msc:57T15
paper · pdf · doi:10.48550/arxiv.math/0210247
41 pages
arxiv created 2002/10/16 · arxiv updated 2009/11/30
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, CP2 # CP2 is a biquotient, but CP4 # HP2 is not. (3) There are only finitely many diffeomorphism classes of 2-connected biquotients in each dimension.