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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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The Stable Homotopy Types of Stunted Lens Spaces mod 4
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by Huajian Yang PDF
Trans. Amer. Math. Soc. 350 (1998), 4775-4798 Request permission

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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Additional Information
  • Huajian Yang
  • Affiliation: Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015
  • Received by editor(s): June 6, 1995
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 4775-4798
  • MSC (1991): Primary 55T15, 55T25
  • DOI: https://doi.org/10.1090/S0002-9947-98-02403-9
  • MathSciNet review: 1624226