LEADER 04285nam 2200613 450 001 9910788890103321 005 20170821171917.0 010 $a1-4704-0730-2 035 $a(CKB)3360000000464501 035 $a(EBL)3113868 035 $a(SSID)ssj0000889222 035 $a(PQKBManifestationID)11482812 035 $a(PQKBTitleCode)TC0000889222 035 $a(PQKBWorkID)10874656 035 $a(PQKB)10867186 035 $a(MiAaPQ)EBC3113868 035 $a(RPAM)4733698 035 $a(PPN)195411986 035 $a(EXLCZ)993360000000464501 100 $a20140905h19851985 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSpectral sequence constructors in algebra and topology /$fD.W. Barnes 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d1985. 210 4$dİ1985 215 $a1 online resource (187 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 53, Number 317 300 $a"Jnauary, 1985, Volume 53, number 317 (fourth of 5 numbers)." 311 $a0-8218-2319-1 320 $aIncludes bibliographical references and index. 327 $a""CONTENTS""; ""PREFACE""; ""I. MODULES OVER HOPE ALGEBRAS""; ""1. Hopf Algebras""; ""2. Groups""; ""3. Lie Algebras""; ""4. Modules""; ""5. Homology and Cohomology""; ""II. CUP PRODUCTS""; ""1. Introduction""; ""2. Relatively Injective Modules""; ""3. Relatively Injective Resolutions""; ""4. General Resolutions""; ""III. SPECTRAL SEQUENCE CONSTRUCTORS""; ""1. Introduction""; ""2. Comparison of Spectral Sequence Constructors""; ""3. Cup Products""; ""IV. FILTRATIONS ON THE NORMALISED STANDARD COMPLEX""; ""1. Introduction""; ""2. Comparison of the Filtrations"" 327 $a""3. Calculation of the E[sub(1)]a???term""""4. Lie Algebras""; ""5. The Adams Spectral Sequence""; ""V. DOUBLE PROJECTIVE RESOLUTIONS""; ""1. The Construction""; ""2. Calculation of the E[sub(1)]a???term""; ""3. Cup Products""; ""VI. PAIR OF RESOLUTIONS""; ""1. Introduction""; ""2. The Coinduced Resolution""; ""3. Cup Products""; ""VII. REPEATED INJECTIVE RESOLUTIONS""; ""1. The Grothendieck Construction""; ""2. Repeated Coinduced Resolutions""; ""VIII. EXPLICIT EQUIVALENCES""; ""1. Survey of Spectral Sequence Constructors""; ""2. Transformation B a??? A*""; ""3. Transformation C a??? A*"" 327 $a""4. Transformation B a??? C""""IX. ACYCLIC MODELS""; ""1. Free Functors""; ""2. Chain Complexes""; ""3 . Filtered Chain Complexes""; ""4. The Uniqueness Theorem""; ""X. COFREE FUNCTORS""; ""1. Free Functors Reformulated""; ""2. Cofree Functors""; ""3. Right Derived Functors""; ""4. Filtered Cochain Complexes""; ""5. The Uniqueness Theorem""; ""XI. LOCAL COEFFICIENTS""; ""1. Homology with Local Coefficients""; ""2. The Uniqueness Theorem""; ""3. Homomorphisms""; ""XII. THE SPECTRAL SEQUENCE OF A FIBRATION""; ""1. Introduction""; ""2. The Classifying Space of a Group""; ""3. Fibrations"" 327 $a""4. Calculation of the E[sup(2)]a???term""""5. Other Constructions""; ""XIII. UNIQUENESS OF THE FIBRATION SPECTRAL SEQUENCE""; ""1. The Fibration Spectral Sequence Constructor Axioms""; ""2. The E[sup(1)][sub(*0)] Axiom""; ""3. The Comparison Theorem""; ""4. The uniqueness Theorem""; ""XIV. SHEAF COHOMOLOGY""; ""1. Sheaves""; ""2. Change of Base""; ""3. Sheaf Cohomology""; ""4. Locally Constant Sheaves""; ""5. The Leray Spectral Sequence""; ""APPENDIX. LIFTING FUNCTIONS""; ""REFERENCES""; ""INDEX""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""K""; ""L""; ""M""; ""N"" 327 $a""P""""Q""; ""R""; ""S""; ""T""; ""U""; ""V"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 53, Number 317. 606 $aFunctor theory 606 $aSpectral sequences (Mathematics) 606 $aHopf algebras 615 0$aFunctor theory. 615 0$aSpectral sequences (Mathematics) 615 0$aHopf algebras. 676 $a512/.55 700 $aBarnes$b D. W$g(Donald W.),$f1935-$044656 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788890103321 996 $aSpectral sequence constructors in algebra and topology$93799693 997 $aUNINA