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

Tel Aviv University

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

All Science Journal Classification (ASJC) codes

General Mathematics

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

Cite this

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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}",

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AU - Shelukhin, Egor

AU - Stojisavljević, Vukašin

PY - 2017/10/1

Y1 - 2017/10/1

N2 - 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.

AB - 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.

KW - Barcode

KW - Floer homology

KW - Hamiltonian diffeomorphism

KW - Persistence module

KW - Symplectic manifold

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

M3 - مقالة

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VL - 17

SP - 757

EP - 786

JO - Moscow Mathematical Journal

JF - Moscow Mathematical Journal

IS - 4

ER -

Persistence modules with operators in morse and floer theory

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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