Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Inertial $h$-cobordisms with finite cyclic fundamental group
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by Terry C. Lawson
Proc. Amer. Math. Soc. 44 (1974), 492-496
DOI: https://doi.org/10.1090/S0002-9939-1974-0358820-2

Abstract:

For $M$ a PL $n$-manifold, $n \geqq 5$, let $I(M)$ be the subset of torsions $\sigma \in \operatorname {Wh} ({\pi _1}M)$ such that the $h$-cobordism $W$ constructed from $M$ with torsion $\sigma$ has its other boundary component PL homeomorphic to $M$. We present three techniques dealing with the determination of $I(M)$ and apply them when ${\pi _1}M = {Z_q}$. We prove: (1) If $n$ is even, ${\pi _1}M \simeq {Z_q},q$ odd, then $I(M) = \operatorname {Wh} ({\pi _1}M)$. (2) If $n$ is odd, then there exists $M$ with ${\pi _1}M \simeq {Z_q}$ such that $I(M) = \operatorname {Wh} ({\pi _1}M)$.
References
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Bibliographic Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 44 (1974), 492-496
  • MSC: Primary 57D80; Secondary 57C10
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0358820-2
  • MathSciNet review: 0358820