Spectral sequence constructors in algebra and topology / / D.W. Barnes

• Record Nr.: UNINA9910828764203321
• Autore: Barnes D. W (Donald W.), <1935->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 1985; ©1985
• ISBN: 1-4704-0730-2
• Descrizione fisica: 1 online resource (187 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 53, Number 317
• Disciplina: 512/.55
• Soggetti: Functor theory; Spectral sequences (Mathematics); Hopf algebras
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "Jnauary, 1985, Volume 53, number 317 (fourth of 5 numbers)."
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: ""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""; ""3. Calculation of the E[sub(1)]â€?term""""4. Lie Algebras""; ""5. The Adams Spectral Sequence""; ""V. DOUBLE PROJECTIVE RESOLUTIONS""; ""1. The Construction""; ""2. Calculation of the E[sub(1)]â€?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 â?? A*""; ""3. Transformation C â?? A*""; ""4. Transformation B â?? 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""; ""4. Calculation of the E[sup(2)]â€?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""; ""P""""Q""; ""R""; ""S""; ""T""; ""U""; ""V""