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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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 ${A_X} \otimes T(U)\xrightarrow { \cong }{H_\ast }(\Omega X)$.
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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