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 Degree Type Dissertation Degree Name Doctor of Philosophy (PhD) Graduate Group Mathematics First Advisor Wolfgang Ziller Subject Categories Geometry and Topology This dissertation is available at ScholarlyCommons: http://repository.upenn.edu/edissertations/311 THE CLASSIFICATION OF SIMPLY CONNECTED BIQUOTIENTS OF DIMENSION AT MOST 7 AND 3 NEW EXAMPLES OF ALMOST POSITIVELY CURVED MANIFOLDS