The Conley index for discrete dynamical systems and the mapping torus

@article{Weilandt2019TheCI,
  title={The Conley index for discrete dynamical systems and the mapping torus},
  author={Frank Weilandt},
  journal={Journal of Applied and Computational Topology},
  year={2019},
  volume={3},
  pages={119-138}
}
  • Frank Weilandt
  • Published 19 January 2018
  • Mathematics
  • Journal of Applied and Computational Topology
The classical Conley index for flows is defined as a certain homotopy type. In the case of a discrete dynamical system, one usually considers the shift equivalence class of the so-called index map. This equivalence relation is rarely used in other contexts and not well understood in general. Here we propose using a topological invariant of the shift equivalence definition: The homotopy type of the mapping torus of the index map. Using a homotopy type offers new ways for comparing Conley indices… 
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