On Eschenburg ’ s Habilitation on biquotient Lectures by Wolfgang Ziller

Topological properties of Eschenburg spaces and 3-Sasakian manifolds

We examine topological properties of the seven-dimensional positively curved Eschenburg biquotients and find many examples which are homeomorphic but not diffeomorphic. A special subfamily of these manifolds also carries a 3-Sasakian metric. Among these we construct a pair of 3-Sasakian spaces which are diffeomorphic to each other, thus giving rise to the first example of a manifold which carri...

On Eschenburg's Habilitation on Biquotients

On M . Mueter ’ s Ph . D . Thesis on Cheeger deformations Lectures

The classification of simply connected biquotients of dimension at most 7 and 3 new examples of almost positively curved manifolds

We classify all compact 1-connected manifolds $M^n$ for $2 \leq n leq 7$ which are diffeomorphic to biquotients. Further, given that $M$ is diffeomorphic to a biquotient, we classify the biquotients it is diffeomorphic to. Finally, we show the homogeneous space $Sp(3)\Sp(1) \tines Sp(1)$ and two of its quotients $Sp(3)\Sp(1) \times Sp(1) \times S^1$ and $\delta S^1 \backslash Sp(3)/Sp(1)\times ...

Cheeger manifolds and the classification of biquotients

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. Every biquotient has a Riemannian metric of nonnegative sectional curvature. In fact, almost all known manifolds of nonnegative curvature are biquotients. The only known closed manifolds of nonnegative sectional curvature which were ...