The Stable Homotopy Types of Stunted Lens Spaces mod 4

Yang, Huajian

doi:10.1090/S0002-9947-98-02403-9

The Stable Homotopy Types of Stunted Lens Spaces mod 4
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by Huajian Yang

Trans. Amer. Math. Soc. 350 (1998), 4775-4798

DOI: https://doi.org/10.1090/S0002-9947-98-02403-9

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Abstract:

Let $L^{n+k}_n$ be the mod $4$ stunted lens space $L^{n+k}/L^{n-1}$. Let $\nu (m)$ denote the exponent of $2$ in $m$, and $\phi (k)$ the number of integers $j$ satisfying $j\equiv 0,1, 2, 4 (\operatorname {mod}8)$, and $0< j\leq k$. In this paper we complete the classification of the stable homotopy types of mod $4$ stunted lens spaces. The main result (Theorem 1.3 (i)) is that, under some appropriate conditions, $L^{n+k}_n$ and $L^{m+k}_m$ are stably equivalent iff $\nu (n-m)\geq \phi (k)+\delta$, where $\delta =-1, 0$ or $1$.

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