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Transactions of the American Mathematical Society

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

 

 

Iterated spinning and homology spheres


Author: Alexander I. Suciu
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
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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

DOI: https://doi.org/10.1090/S0002-9947-1990-0987169-3
Keywords: $ p$-spinning, homology sphere, homotopy type
Article copyright: © Copyright 1990 American Mathematical Society