%0 Journal Article
%A Hernández Corbato, Luis
%A Le Calvez , Patrice
%A Romero Ruiz del Portal, Francisco
%T About the homological discrete Conley index of isolated invariant acyclic continua
%D 2013
%@ 1465-3060
%U https://hdl.handle.net/20.500.14352/33437
%X This article includes an almost self-contained exposition on the discrete Conley index and its duality. We work with a locally defined homeomorphism f in R-d and an acyclic continuum X, such as a cellular set or a fixed point, invariant under f and isolated. We prove that the trace of the first discrete homological Conley index of f and X is greater than or equal to -1 and describe its periodical behavior. If equality holds then the traces of the higher homological indices are 0. In the case of orientation-reversing homeomorphisms of R-3, we obtain a characterization of the fixed point index sequence {i(f(n) (,) p}n >= 1 for a fixed point p which is isolated as an invariant set. In particular, we obtain that i(f , p) <= 1. As a corollary, we prove that there are no minimal orientation-reversing homeomorphisms in R-3.
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