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About the homological
discrete Conley index of isolated invariant acyclic
continua
Luis Hernández-Corbato, Patrice Le Calvez and Francisco R Ruiz del Portal |
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Geometry & Topology 17 (2013) 2977–3026
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Abstract |
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This article includes an almost self-contained exposition on the discrete Conley index and its duality. We work with a locally defined homeomorphism in and an acyclic continuum , such as a cellular set or a fixed point, invariant under and isolated. We prove that the trace of the first discrete homological Conley index of and is greater than or equal to 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 , we obtain a characterization of the fixed point index sequence for a fixed point which is isolated as an invariant set. In particular, we obtain that . As a corollary, we prove that there are no minimal orientation-reversing homeomorphisms in . |
Keywords
fixed point index, Conley index, filtration pairs
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Mathematical Subject Classification 2010
Primary: 37B30, 37C25, 54H25
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References |
Publication
Received: 6 February 2013
Revised: 24 June 2013
Accepted: 26 June 2013
Published: 17 October 2013
Proposed: Yasha Eliashberg
Seconded: Leonid Polterovich, Steve Ferry
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Authors |
| Luis Hernández-Corbato | |
| Departamento de Geometría y
Topología Universidad Complutense de Madrid Plaza de Ciencias 3 28040 Madrid Spain |
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| Patrice Le Calvez | |
| Institut de Mathematiques de
Jussieu Université Pierre et Marie Curie UMR 7586 CNRS Case 247, 4, place Jussieu 75252 Paris France |
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| Francisco R Ruiz del Portal | |
| Departamento de Geometría y
Topología Universidad Complutense de Madrid Plaza de Ciencias 3 28040 Madrid Spain |
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| http://www.mat.ucm.es/~rrportal/ | |
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