@article{54b933ba65244518864bf275a16eefd4,
title = "Persistence modules with operators in morse and floer theory",
abstract = "We introduce a new notion of persistence modules endowed with operators. It encapsulates the additional structure on Floer-type persistence modules coming from the intersection product with classes in the ambient (quantum) homology, along with a few other geometric situations. We provide sample applications to the C˚-geometry of Morse functions and to Hofer{\textquoteright}s geometry of Hamiltonian diffeomorphisms that go beyond spectral invariants and traditional persistent homology.",
keywords = "Barcode, Floer homology, Hamiltonian diffeomorphism, Persistence module, Symplectic manifold",
author = "Leonid Polterovich and Egor Shelukhin and Vuka{\v s}in Stojisavljevi{\'c}",
note = "Publisher Copyright: {\textcopyright} 2017 Independent University of Moscow.",
year = "2017",
month = oct,
day = "1",
doi = "10.17323/1609-4514-2017-17-4-757-786",
language = "אנגלית",
volume = "17",
pages = "757--786",
journal = "Moscow Mathematical Journal",
issn = "1609-3321",
publisher = "Independent University of Moscow",
number = "4",
}