Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On the group $ {\rm SSF}(G),\;G$ a cyclic group of prime order

Authors: M. Maller and J. Whitehead
Journal: Trans. Amer. Math. Soc. 290 (1985), 725-733
MSC: Primary 58F09; Secondary 20C99
MathSciNet review: 792823
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Abstract: We extend the definition of the obstruction group $ {\text{SSF}}(G)$ in the case where $ G$ is a cyclic group of prime order. We show that an endomorphism of a free $ ZG$-module is a direct summand of a virtual permutation if its characteristic polynomial has the appropriate form. Among these endomorphisms the virtual permutations are detected by $ {K_0}$. The main application is in detecting Morse-Smale isotopy classes.

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Keywords: Morse-Smale diffeomorphism, virtual permutation, group rings
Article copyright: © Copyright 1985 American Mathematical Society