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About the homological discrete Conley index of isolated invariant acyclic continua | | Luis Hernández-Corbato
; Patrice Le Calvez
; Francisco R. Ruiz del Portal
; | | Date: |
5 Feb 2013 | | Abstract: | This article includes an almost self-contained exposition on the discrete
Conley index and its duality. We work with a local homeomorphism of
$mathds{R}^d$ and an invariant and isolated acyclic continuum, such as a
cellular set or a fixed point. In this setting, we obtain a complete
description of the first discrete homological Conley index, which is periodic,
that enforces a combinatorial behavior of higher indices. As a consequence, we
prove that isolated (as an invariant set) fixed points of orientation-reversing
homeomorphisms of $mathds{R}^3$ have fixed point index $le 1$ and, as a
corollary, that there are no minimal orientation-reversing homeomorphisms in
$mathds{R}^3$. | | Source: | arXiv, 1302.1137 | | Services: | Forum | Review | PDF | Favorites | |
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