The symplectic cohomology of magnetic cotangent bundles

Yoel Groman; Will J. Merry

doi:https://doi.org/10.4171/CMH/555

The symplectic cohomology of magnetic cotangent bundles

Yoel Groman, Will J. Merry

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

Abstract

We construct a family version of symplectic Floer cohomology for magnetic cotangent bundles, without any restrictions on the magnetic form, using the dissipative method for compactness introduced by Groman (2023). As an application, we deduce that if N is a closed orientable manifold and σ is a magnetic form that is not weakly exact, then the π1-sensitive Hofer-Zehnder capacity of any compact set in the magnetic cotangent bundle determined by σ is finite.

Original language	English
Pages (from-to)	365-424
Number of pages	60
Journal	Commentarii Mathematici Helvetici
DOIs	https://doi.org/10.4171/CMH/555
State	Published - 2023

Keywords

Hofer-Zehnder capacity
Twisted symplectic cohomology
family Floer theory

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

https://doi.org/10.4171/CMH/555

Cite this

@article{f1df532add2346048202b5d810981057,

title = "The symplectic cohomology of magnetic cotangent bundles",

abstract = "We construct a family version of symplectic Floer cohomology for magnetic cotangent bundles, without any restrictions on the magnetic form, using the dissipative method for compactness introduced by Groman (2023). As an application, we deduce that if N is a closed orientable manifold and σ is a magnetic form that is not weakly exact, then the π1-sensitive Hofer-Zehnder capacity of any compact set in the magnetic cotangent bundle determined by σ is finite.",

keywords = "Hofer-Zehnder capacity, Twisted symplectic cohomology, family Floer theory",

author = "Yoel Groman and Merry, {Will J.}",

note = "Publisher Copyright: {\textcopyright} 2023 Swiss Mathematical Society.",

year = "2023",

doi = "https://doi.org/10.4171/CMH/555",

language = "الإنجليزيّة",

pages = "365--424",

journal = "Commentarii Mathematici Helvetici",

issn = "0010-2571",

publisher = "European Mathematical Society Publishing House",

}

TY - JOUR

T1 - The symplectic cohomology of magnetic cotangent bundles

AU - Groman, Yoel

AU - Merry, Will J.

PY - 2023

Y1 - 2023

N2 - We construct a family version of symplectic Floer cohomology for magnetic cotangent bundles, without any restrictions on the magnetic form, using the dissipative method for compactness introduced by Groman (2023). As an application, we deduce that if N is a closed orientable manifold and σ is a magnetic form that is not weakly exact, then the π1-sensitive Hofer-Zehnder capacity of any compact set in the magnetic cotangent bundle determined by σ is finite.

AB - We construct a family version of symplectic Floer cohomology for magnetic cotangent bundles, without any restrictions on the magnetic form, using the dissipative method for compactness introduced by Groman (2023). As an application, we deduce that if N is a closed orientable manifold and σ is a magnetic form that is not weakly exact, then the π1-sensitive Hofer-Zehnder capacity of any compact set in the magnetic cotangent bundle determined by σ is finite.

KW - Hofer-Zehnder capacity

KW - Twisted symplectic cohomology

KW - family Floer theory

UR - http://www.scopus.com/inward/record.url?scp=85174239603&partnerID=8YFLogxK

U2 - https://doi.org/10.4171/CMH/555

DO - https://doi.org/10.4171/CMH/555

M3 - مقالة

SN - 0010-2571

SP - 365

EP - 424

JO - Commentarii Mathematici Helvetici

JF - Commentarii Mathematici Helvetici

ER -

The symplectic cohomology of magnetic cotangent bundles

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this