Cofibrations of algebras
Copyright policy )Cofibrations of algebras
The chain complex of a twisted free product A*t, FK, is chain homotopy equivalent to a differential graded algebra, which is identified to be a confibration of algebras as defined by Quillen. Under certain connectivity conditions we obtain a long exact sequence connecting the homologies of A, K, and A*t FK. In particular we derive a long exact sequence connecting the homologies of ΩY, ΩΣX and Ω(Y Ug CX) (Ω, C, Σ are the loop, the cone and the suspension constructions respectively). A chain complex equivalent to the chain complex of the Milnor free group FX is recognized, from which results a theorem of Bott and Samelson that H(ΩΣX) is freely generated as a graded algebra by H(X).
cofibration of algebras, Homological algebra in category theory, derived categories and functors, twisted free tensor product, homology of the loop space of a suspension, Graded rings and modules (associative rings and algebras), Modules of differentials, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), loop space, differential graded algebra, Homology and cohomology of \(H\)-spaces, chain complex of a twisted free product, Loop spaces
cofibration of algebras, Homological algebra in category theory, derived categories and functors, twisted free tensor product, homology of the loop space of a suspension, Graded rings and modules (associative rings and algebras), Modules of differentials, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), loop space, differential graded algebra, Homology and cohomology of \(H\)-spaces, chain complex of a twisted free product, Loop spaces
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