Fixed Point Index in Symmetric Products
نویسنده
چکیده
Let U be an open subset of a locally compact metric ANR X and let f : U → X be a continuous map. In this paper we study the fixed point index of the map that f induces in the n-symmetric product of X, Fn(X). This index can detect the existence of periodic orbits of period ≤ n of f , and it can be used to obtain the Euler characteristic of the n-symmetric product of a manifold X, χ(Fn(X)). We compute χ(Fn(X)) for all orientable compact surfaces without boundary.
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