Table of Contents The Siegel Modular Variety of Degree Two and Level Four 0. Introduction 3 1. Algebraic Background 7 2. Geometric Background 17 3. Taking Stock 28 4. Type III A 30 5. Type II A 35 6. Type II B 38 7. Type IV C 47 8. Summing up 52 Appendix. An exact sequence in homology 56 References 57 Cohomology of the Siegel Modular Group of Degree Two and Level Four 1. Introduction 61 2. The Building 64 3. Cycles 65 4. The Main Theorems 67 References 74 Vll
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