Loop Space Homology of Spaces of Small Category

Félix, Yves;Thomas, JC.
(1993) Transactions of the American mathematical society — Vol. 338, n° 2, p. 711-721 (1993)

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  • Félix, YvesUCLouvain
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  • Thomas, JC.
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Abstract
Only little is known concerning H*(OMEGAX; k) , the loop space homology of a finite CW complex X with coefficients in a field k. A space X is called an r-cone if there exists a filtration * = X0 subset-of X1 subset-of ... subset-of X(r) = X, such that X(i) has the homotopy type of the cofibre of a map from a wedge of sphere into X(i-1). Denote by A(X) the sub-Hopf algebra image of H*(OMEGAX1). We prove then that for a graded r-cone, r less-than-or-equal-to 3, there exists an isomorphism A(X) x T(U) --> congruent-to H*(OMEGAX).
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Félix, Y., & Thomas, JC. (1993). Loop Space Homology of Spaces of Small Category. Transactions of the American mathematical society, 338(2), 711-721. https://doi.org/10.2307/2154425 (Original work published 1993)