| Preface Chapter 1.Conventions 1.Vector Spaces 2.Algebras, Coalgebras, and Modules 3.Dual Modules 4.Bialgebras and Hopf Algebras 5.O－Modules and Relative Homological Algebra 6.Algebras with Coproducts 7.Chains and Cochains 8.Differential Algebras and Coalgebras 9.Simplicial O-Modules 10.Homology of Simplicial Sets and Simplicial Groups 11.Cotriples, Simplicial Objects, and Projective Resolutions 12.Simplicial O-Coalgebras and Steenrod Operations 13.Steenrod Operations on the Cohomology of Simplicial Sets 14.Steenrod Operations on the Cohomology of Hopf Algebras 15.Bisimplicial Objects 16.The Spectral Sequence of a Bisimplicial @-Module 17.Cup-k Products and Bisimplicial O-Modules Chapter 2.The Spectral Sequence of a Bisimplicial Coalgebra 1.Bisimplicial O-Coalgebras 2.Filtrations 3.The Spectral Sequence 4.Bisimplicial Sets with Group Action 5.Application to the Serre Spectral Sequence 6.Application to Andre-Quillen Cohomology Chapter 3.Bialgebra Actions on the Cohomology of Algebras 1.Left Action by a Bialgebra 2.Left Action by an Algebra with Coproducts 3.Right Action by a Hopf algebra Chapter 4.Extensions of Hopf Algebras 1.Convolutions and Conjugations 2.Some Properties of Extensions 3.Adjunction Isomorphism and Change-of-Rings Spectral Sequence Chapter 5.Steenrod Operations in the Change-of-Rings Spectral Sequence 1.The Spectral Sequence with its Products and Steenrod Squares 2.Steenrod Operations on Ext 3.Central Extensions 4.The Operations at the E2-1evel 5.A Simple Example 6.Application to the Cohomology of the Steenrod Algebra 7.Application to Finite sub-Hopf Algebras of the Steenrod Algebra 8.Applications to the Cohomology of Groups Chapter 6.The Eilenberg-Moore Spectral Sequence 1.Kan Fibrations and Twisted Cartesian Products 2.Bisimplicial Models for Fiber Bundles 3.Construction of the Spectral Sequence 4.Calculation of the E2-Term Chapter 7.Steenrod Operations in the Eilenberg-Moore Spectral Sequence 1.The Spectral Sequence with its Products and Steenrod Squares 2. Steenrod Operations on Ext 3.The Operations at the E2-1evel 4.Applications Bibliography Index |
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