Date of Award
Doctor of Philosophy (PhD)
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.
DeVito, Jason, "The classification of simply connected biquotients of dimension at most 7 and 3 new examples of almost positively curved manifolds" (2011). Publicly Accessible Penn Dissertations. 311.