Topological classification of oriented cycles of linear mappings

We consider the problem of classifying oriented cycles of linear mappings $F^pto F^qtodotsto F^rto F^p$ over a field $F$ of complex or real numbers up to homeomorphisms in the spaces $F^p,F^q,dots,F^r$. We reduce it to the problem of classifying linear operators $F^nto F^n$ up to homeomorphism in $F^n$, which was studied by N.H. Kuiper and J.W. Robbin [Invent. Math. 19 (2) (1973) 83-106] and by other authors.