Persistence modules with operators in morse and floer theory

Leonid Polterovich; Egor Shelukhin; Vukašin Stojisavljević

doi:10.17323/1609-4514-2017-17-4-757-786

Persistence modules with operators in morse and floer theory

Leonid Polterovich, Egor Shelukhin, Vukašin Stojisavljević

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	757-786
Number of pages	30
Journal	Moscow Mathematical Journal
Volume	17
Issue number	4
DOIs	https://doi.org/10.17323/1609-4514-2017-17-4-757-786
State	Published - 1 Oct 2017

Keywords

Barcode
Floer homology
Hamiltonian diffeomorphism
Persistence module
Symplectic manifold

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10.17323/1609-4514-2017-17-4-757-786

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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.",

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author = "Leonid Polterovich and Egor Shelukhin and Vuka{\v s}in Stojisavljevi{\'c}",

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KW - Floer homology

KW - Hamiltonian diffeomorphism

KW - Persistence module

KW - Symplectic manifold

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Persistence modules with operators in morse and floer theory

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