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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Virtual permutations of $\textbf {Z}[\textbf {Z}^{n}]$ complexes
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by Michael Maller and Jennifer Whitehead PDF
Proc. Amer. Math. Soc. 90 (1984), 162-166 Request permission

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
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 90 (1984), 162-166
  • MSC: Primary 58F09; Secondary 20C07
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0722437-4
  • MathSciNet review: 722437