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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Inertial $ h$-cobordisms with finite cyclic fundamental group


Author: Terry C. Lawson
Journal: Proc. Amer. Math. Soc. 44 (1974), 492-496
MSC: Primary 57D80; Secondary 57C10
MathSciNet review: 0358820
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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)$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0358820-2
PII: S 0002-9939(1974)0358820-2
Keywords: Inertial $ h$-cobordism, $ s$-cobordism theorem, Whitehead group, Wall group, pseudo-projective plane
Article copyright: © Copyright 1974 American Mathematical Society