Persistent homology and Floer-Novikov theory

@article{Usher2015PersistentHA,
  title={Persistent homology and Floer-Novikov theory},
  author={M. Usher and J. Zhang},
  journal={arXiv: Symplectic Geometry},
  year={2015}
}
  • M. Usher, J. Zhang
  • Published 2015
  • Mathematics
  • arXiv: Symplectic Geometry
  • We construct "barcodes" for the chain complexes over Novikov rings that arise in Novikov's Morse theory for closed one-forms and in Floer theory on not-necessarily-monotone symplectic manifolds. In the case of classical Morse theory these coincide with the barcodes familiar from persistent homology. Our barcodes completely characterize the filtered chain homotopy type of the chain complex; in particular they subsume in a natural way previous filtered Floer-theoretic invariants such as boundary… CONTINUE READING
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