Loop space homology of spaces of small category
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- by Yves FĂ©lix and Jean-Claude Thomas PDF
- Trans. Amer. Math. Soc. 338 (1993), 711-721 Request permission
Abstract:
Only little is known concerning ${H_\ast }(\Omega X;{\mathbf {k}})$, the loop space homology of a finite ${\text {CW}}$ complex $X$ with coefficients in a field ${\mathbf {k}}$. A space $X$ is called an $r$-cone if there exists a filtration $\ast = {X_0} \subset {X_1} \subset \cdots \subset {X_r} = X$, 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 ${H_\ast }(\Omega {X_1})$. We prove then that for a graded $r$-cone, $r \leq 3$, there exists an isomorphism ${A_X} \otimes T(U)\xrightarrow { \cong }{H_\ast }(\Omega X)$.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 338 (1993), 711-721
- MSC: Primary 55P35; Secondary 16E10, 55P62, 57T25
- DOI: https://doi.org/10.1090/S0002-9947-1993-1134757-2
- MathSciNet review: 1134757