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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Properties of Anick’s spaces
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by Stephen D. Theriault PDF
Trans. Amer. Math. Soc. 353 (2001), 1009-1037 Request permission

Abstract:

We prove three useful properties of Anick’s space $T^{2n-1}(p^{r})$. First, at odd primes a map from $P^{2n}(p^{r})$ into a homotopy commutative, homotopy associative $H$-space $X$ can be extended to a unique $H$-map from $T^{2n-1}(p^{r})$ into $X$. Second, at primes larger than $3$, $T^{2n-1}(p^{r})$ is itself homotopy commutative and homotopy associative. And third, the first two properties combine to show that the order of the identity map on $T^{2n-1}(p^{r})$ is $p^{r}$.
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Additional Information
  • Stephen D. Theriault
  • Affiliation: Department of Mathematics, University of Illinois at Chicago, Chicago, Illinois 60607
  • Address at time of publication: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22903
  • MR Author ID: 652604
  • Email: st7b@virginia.edu
  • Received by editor(s): December 4, 1998
  • Published electronically: August 8, 2000
  • Additional Notes: The author was supported in part by an NSERC Postdoctoral Fellowship.
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 1009-1037
  • MSC (2000): Primary 55P45; Secondary 55Q15
  • DOI: https://doi.org/10.1090/S0002-9947-00-02623-4
  • MathSciNet review: 1709780