Transactions of the American Mathematical Society

Author(s): José M. Salazar
Journal: Trans. Amer. Math. Soc. 357 (2005), 3493-3508.
MSC (2000): Primary 54H20, 54H25
Posted: September 2, 2004
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Abstract: Let

be an open subset of a locally compact metric ANR

and let $f:U \rightarrow X$ be a continuous map. In this paper we study the fixed point index of the map that

induces in the

-symmetric product of

, $F_{n}(X)$ . This index can detect the existence of periodic orbits of period $\leq n$ of

, and it can be used to obtain the Euler characteristic of the

-symmetric product of a manifold

, $\chi(F_{n}(X))$ . We compute $\chi(F_{n}(X))$ for all orientable compact surfaces without boundary.

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