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 $\delta S^1 \backslash Sp(3)/Sp(1)\times Sp(1)$ admit metrics of almost positive curvature. iv