Geometry & Topology
- Geom. Topol.
- Volume 17, Number 5 (2013), 2977-3026.
About the homological discrete Conley index of isolated invariant acyclic continua
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 .
Geom. Topol. Volume 17, Number 5 (2013), 2977-3026.
Received: 6 February 2013
Revised: 24 June 2013
Accepted: 26 June 2013
First available in Project Euclid: 20 December 2017
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Hernández-Corbato, Luis; Le Calvez, Patrice; R Ruiz del Portal, Francisco. About the homological discrete Conley index of isolated invariant acyclic continua. Geom. Topol. 17 (2013), no. 5, 2977--3026. doi:10.2140/gt.2013.17.2977. https://projecteuclid.org/euclid.gt/1513732693