EXAMPLES OF ALMOST POSITIVELY CURVED MANIFOLDS

Where do I even begin? There are so many people without whom this thesis would never have come into existence. Let me start with the primary mathematical con-tributors. This list must, of course, begin with my amazing advisor Wolfgang Ziller. Between the weekly individual meetings and the department’s worst kept secret, the ”secret seminar”, I had just the right impetus to keep making progress not only on my thesis, but in my understanding of geometry as a whole. To the secret seminar crowd, both current and past- Lee, Marco, Ricardo, Chenxu, John, Martin, Corey, Will, Jeffrey, Luigi, and all the other more sporadic attenders, I am sure I have plagued you with more questions than I should have and I thank you for both your answers and your patience. To the rest of the math department, I thank you as well for you ear at pizza seminar and your help, especially during my first and second year classes. To the office staff, Janet, Monica, Paula, and Robin, without you all, the de-partment would cease functioning. I don’t think we really appreciate how hard it is to put up with all of us “crazy mathematicians”. I also want to thank you fo