Properties of Anick’s spaces

Theriault, Stephen

doi:10.1090/S0002-9947-00-02623-4

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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