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Proceedings of the American Mathematical Society

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



Virtual permutations of $\textbf {Z}[\textbf {Z}^{n}]$ complexes

Authors: Michael Maller and Jennifer Whitehead
Journal: Proc. Amer. Math. Soc. 90 (1984), 162-166
MSC: Primary 58F09; Secondary 20C07
MathSciNet review: 722437
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Abstract: We extend the characterization of virtual permutation endomorphisms in the case where ${\prod _1}(M) = {Z^n}$. We show that for endomorphisms of $Z[{Z^n}]$ complexes the appropriate eigenvalue condition is that all eigenvalues be roots of units of the group ring $Z[{Z^n}]$. Among these endomorphisms the virtual permutations are detected by ${K_0}$. The main application is in identifying Morse-Smale isotopy classes on these manifolds.

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Keywords: Virtual permutation, Morse-Smale, SSF, group rings
Article copyright: © Copyright 1984 American Mathematical Society