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On four-dimensional $ h$-cobordism


Author: Sławomor Kwasik
Journal: Proc. Amer. Math. Soc. 97 (1986), 352-354
MSC: Primary 57R80; Secondary 57N13, 57S17
DOI: https://doi.org/10.1090/S0002-9939-1986-0835897-7
MathSciNet review: 835897
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Abstract: The influence of the Poincaré Conjecture on the following problem of M. Cohen is examined.

Problem. Does there exist a four-dimensional $ h$-cobordism with nontrivial Whitehead torsion?

It is proved (assuming the Poincarè Conjecture) that none of the following groups may be the fundamental group of a $ 4$-dimensional $ h$-corbordism with nontrivial Whitehead torsion: generalized quaternion groups, cyclic groups $ {Z_8}$, $ {Z_{12}}$, the binary octahedral group, the binary tetrahedral group.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0835897-7
Article copyright: © Copyright 1986 American Mathematical Society

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