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Properties of Anick's spaces


Author: Stephen D. Theriault
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
Published electronically: August 8, 2000
MathSciNet review: 1709780
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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
Email: st7b@virginia.edu

DOI: https://doi.org/10.1090/S0002-9947-00-02623-4
Keywords: $H$-spaces, universal Whitehead product, exponent
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.
Article copyright: © Copyright 2000 American Mathematical Society

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