Contents Abstract vii Preface ix Acknowledgements xiii Part 1 The Homology and Homotopy Theory Associated with QBTT^ Chapter 1. Introduction 3 1.1. Statement of Results 3 1.2. Organization of Part 1 6 Chapter 2. Preliminaries 7 2.1. Some Facts on the R-Completion Functor 7 2.2. Mod-R Acyclic Spaces and Proposition 1.1.2 7 2.3. The Quillen "Plus" Construction 8 Chapter 3. A model for S*ttX£ 9 3.1. An Algebraic "Plus" Construction 9 3.2. Proof of Theorems 1.1.2 and 1.1.3 12 Chapter 4. Homology Exponents for QBiTp 13 4.1. Extended Maps and Homotopies 13 4.2. Proof of Theorem 1.1.1 15 Chapter 5. Examples for Homology Exponents 21 5.1. Groups with a Dihedral Sylow 2-Subgroup 21 5.2. Groups with a Semidihedral Sylow 2-Subgroup 23 Chapter 6. The Homotopy Groups of BTT^ 25 6.1. Some Basic Facts 25 6.2. Proof of Theorem 1.1.4 27 6.3. Examples for Homotopy Exponents 28
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