Date of Award

Spring 5-16-2011

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Mathematics

First Advisor

Wolfgang Ziller

Abstract

We classify all compact 1-connected manifolds $M^n$ for $2 \leq n leq 7$ which are
di ffeomorphic to biquotients. Further, given that $M$ is di ffeomorphic to a biquotient,
we classify the biquotients it is diff eomorphic 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.
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