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Transactions of the American Mathematical Society

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



The Stable Homotopy Types of Stunted Lens Spaces mod 4

Author: Huajian Yang
Journal: Trans. Amer. Math. Soc. 350 (1998), 4775-4798
MSC (1991): Primary 55T15, 55T25
MathSciNet review: 1624226
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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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Huajian Yang
Affiliation: Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015

Received by editor(s): June 6, 1995
Article copyright: © Copyright 1998 American Mathematical Society