Iterated spinning and homology spheres

Suciu, Alexander I.

doi:10.1090/S0002-9947-1990-0987169-3

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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