TABLE OF CONTENTS

1. Introduction 1

2. Fundamental families 9

3. The Kunneth spectral sequence: special cases 23

4. Geometric projective resolutions 38

5. Construction of the Kunneth spectral sequence 43

6. Some consequences of the Kunneth spectral sequence 46

7. The Universal Coefficient spectral sequence:

special cases 50

8. Geometric infective resolutions 58

9. Construction of the Universal Coefficient

spectral sequence 68

10. Applications: KK -equivalence 73

11. Applications: mod p equivariant K-theory 82

References 90