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

 

Virtual permutations of $ {\bf Z}[{\bf Z}\sp{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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0722437-4
PII: S 0002-9939(1984)0722437-4
Keywords: Virtual permutation, Morse-Smale, SSF, group rings
Article copyright: © Copyright 1984 American Mathematical Society