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Fixed point index in symmetric products |
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| Authors: | José M Salazar |
| Institution: | Departamento de Matemáticas, Universidad de Alcalá, Alcalá de Henares, Madrid 28871, Spain |
| Abstract: | Let  be an open subset of a locally compact metric ANR  and let  be a continuous map. In this paper we study the fixed point index of the map that  induces in the  -symmetric product of  ,  . This index can detect the existence of periodic orbits of period  of  , and it can be used to obtain the Euler characteristic of the  -symmetric product of a manifold  ,  . We compute  for all orientable compact surfaces without boundary. |
| Keywords: | Fixed point index hyperspaces symmetric product semidynamical systems |
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