On the group 𝑆𝑆𝐹(𝐺),𝐺 a cyclic group of prime order

Maller, M.; Whitehead, J.

doi:10.1090/S0002-9947-1985-0792823-0

On the group $\textrm {SSF}(G),\;G$ a cyclic group of prime order
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by M. Maller and J. Whitehead PDF

Trans. Amer. Math. Soc. 290 (1985), 725-733 Request permission

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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