Persistence modules with operators in morse and floer theory

Leonid Polterovich, Egor Shelukhin, Vukašin Stojisavljević

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

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’s geometry of Hamiltonian diffeomorphisms that go beyond spectral invariants and traditional persistent homology.

Original languageEnglish
Pages (from-to)757-786
Number of pages30
JournalMoscow Mathematical Journal
Volume17
Issue number4
DOIs
StatePublished - 1 Oct 2017

Funding

FundersFunder number
National Science FoundationDMS-1128155
European Research Council338809

    Keywords

    • Barcode
    • Floer homology
    • Hamiltonian diffeomorphism
    • Persistence module
    • Symplectic manifold

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