Conley–Morse–Forman Theory for Combinatorial Multivector Fields on Lefschetz Complexes

@article{Mrozek2017ConleyMorseFormanTF,
  title={Conley–Morse–Forman Theory for Combinatorial Multivector Fields on Lefschetz Complexes},
  author={Marian Mrozek},
  journal={Foundations of Computational Mathematics},
  year={2017},
  volume={17},
  pages={1585-1633}
}
  • M. Mrozek
  • Published 29 May 2015
  • Mathematics, Computer Science
  • Foundations of Computational Mathematics
We introduce combinatorial multivector fields, associate with them multivalued dynamics and study their topological features. Our combinatorial multivector fields generalize combinatorial vector fields of Forman. We define isolated invariant sets, Conley index, attractors, repellers and Morse decompositions. We provide a topological characterization of attractors and repellers and prove Morse inequalities. The generalization aims at algorithmic analysis of dynamical systems through… 
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We extend discrete Morse-Bott theory to the setting of loop-free (or acyclic) categories. First of all, we state a homological version of Quillen’s Theorem A in this context and introduce the notion
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