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Transactions of the American Mathematical Society

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Fixed point index in symmetric products

Author: José M. Salazar
Journal: Trans. Amer. Math. Soc. 357 (2005), 3493-3508
MSC (2000): Primary 54H20, 54H25
Published electronically: September 2, 2004
MathSciNet review: 2146635
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Abstract: Let $U$ be an open subset of a locally compact metric ANR $X$ and let $f:U \rightarrow X$ 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 $X$, $F_{n}(X)$. This index can detect the existence of periodic orbits of period $\leq n$ of $f$, and it can be used to obtain the Euler characteristic of the $n$-symmetric product of a manifold $X$, $\chi(F_{n}(X))$. We compute $\chi(F_{n}(X))$ for all orientable compact surfaces without boundary.

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Additional Information

José M. Salazar
Affiliation: Departamento de Matemáticas, Universidad de Alcalá, Alcalá de Henares, Madrid 28871, Spain

Keywords: Fixed point index, hyperspaces, symmetric product, semidynamical systems
Received by editor(s): May 23, 2003
Received by editor(s) in revised form: October 22, 2003
Published electronically: September 2, 2004
Article copyright: © Copyright 2004 American Mathematical Society

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