Properties of geometrical objects which are invariant under (small) perturbations are a major subject of research in algebraic topology. As a special but typical case the fixed-point equation F(x)=x is discussed here from this point of view. The classical fixed-point index is one such invariant. It turns out to be the universal invariant with respect to a rather natural notion of perturbation. Finer invariants can be obtained if the class of permissible perturbations is restricted. The case of perturbations with symmetries is discussed in more detail.
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References
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(References 2, 5 and 6 contain many more references on our subject)
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