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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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Iterated spinning and homology spheres
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by Alexander I. Suciu PDF
Trans. Amer. Math. Soc. 321 (1990), 145-157 Request permission

Abstract:

Given a closed $n$-manifold ${M^n}$ and a tuple of positive integers $P$, let ${\sigma _P}M$ be the $P$-spin of $M$. If ${M^n} \not \backsimeq {S^n}$ and $P \ne Q$ (as unordered tuples), it is shown that ${\sigma _P}M\not \backsimeq {\sigma _Q}M$ if either (1) ${H_*}({M^n})\not \cong {H_*}({S^n})$, (2)${\pi _1}M$ finite, (3) $M$ aspherical, or (4) $n = 3$. Applications to the homotopy classification of homology spheres and knot exteriors are given.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 321 (1990), 145-157
  • MSC: Primary 57N65; Secondary 55Q52, 57Q45, 57R19
  • DOI: https://doi.org/10.1090/S0002-9947-1990-0987169-3
  • MathSciNet review: 987169