The Homology of Hopf Spaces (North-Holland Mathematical Library)

This exposition of the theory of finite Hopf spaces details the development of the subject over the last thirty years, with the homology of such spaces as its main theme. The three chief areas of study in the volume are: - The study of finite H-spaces with torsion free integral homology. - The study of finite H-spaces with homology torsion. - The construction of finite H-spaces. INTRODUCTION......Page 5 PART I: HOPF ALGEBRAS......Page 10 § 1 HOPF ALGEBRAS......Page 12 §2: DEroMPaSITIONS OF HOPF ALGEBRAS......Page 25 §3 COVERING SPACES......Page 32 §4 POINCARE AND S-DUALITY......Page 38 PART II: CLA SSIFYING SPACES......Page 45 §5: LOOP SPACES AND CLASSIFYING SPACES......Page 47 §6: A -SPACES......Page 55 §7: THE COHOMOLOGY OF CLASSIFYING SPACES......Page 66 §8: THE RATIONAL roHOMOLOGY OF LOOP SPACES......Page 72 PART III: LOCALIZATION......Page 77 §9: LOCALIZATION......Page 79 §10 LOCALIZATION AND H-SPACES......Page 88 PART IV: THE BOCKSfEIN SPECTRAL SEQUENCE......Page 98 § 11: TIlE BOCKSfEIN SPECfRAL SEQUENCE......Page 100 §l2: IMPLICATIONS AND THE BOCKSTEIN SPECTRAL SEQUENCE......Page 103 §13: DIFFERENTIAL HOPF ALGEBRAS......Page 114 §14:MORAVA K-THEORY......Page 122 PART V: THE PROJECfIVE PLANE......Page 127 §15: THE PROJECTIVE PLANE......Page 129 §16: STEENROD SQUARES AND TRUNCAlED POLYNOMIAL ALGEBRAS......Page 134 §17: STEENROD SQUARES AND PRIMITIVELY GENERATED CDHOMOLOGY......Page 140 §18: K-TIIEORY AND TORSION FREE H-SPACES......Page 145 §19: HOMOTOPY COMMlITATIVE H-SPACES......Page 148 PART VI: REFLECrION GROUPS AND CLASSIFYING SPACES......Page 151 §20 REFLECfION GROUPS AND INVARIANT THEORY......Page 153 §21 REAL REFLECfION GROUPS......Page 159 §22: ruMPLEX AND P-ADIC REFLECfION GROUPS......Page 165 §23: MOD P REFLECfION GROUPS......Page 172 §24:RINGS OF INVARIANTS AS THE roHOMOLOGY OF CLASSIFYING SPACES......Page 177 §25: ALGEBRAIC CLOSURES......Page 183 §26 INSEPARABLE EXlENSIONS......Page 193 §27: GALOIS THEORY......Page 198 §28: CLASSIFYING SPACES WIlli TORSION......Page 205 PART VII: SEalNDARY OPERATIONS......Page 211 §29: TIIE ElLENBERG-MOORE SPECfRAL SEQUENCE......Page 213 §30: SECONDARY COHOMOLOGY OPERATIONS......Page 221 §31: H-SPACES Willi PRIMITIVELY GENERATED COHOMOL