Semi-global Kuranishi charts and the definition of contact homology

Erkao Bao; Ko Honda

doi:10.1016/j.aim.2023.108864

Semi-global Kuranishi charts and the definition of contact homology

Erkao Bao, Ko Honda

School of Mathematics

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

6 Scopus citations

Abstract

We define the contact homology algebra for any contact manifold and show that it is an invariant of the contact manifold. More precisely, given a contact manifold (M,ξ) and some auxiliary data D, we define an algebra HC(D). If D₁ and D₂ are two choices of auxiliary data for (M,ξ), then HC(D₁) and HC(D₂) are isomorphic. We use a simplified version of Kuranishi perturbation theory, consisting of semi-global Kuranishi charts.

Original language	English (US)
Article number	108864
Journal	Advances in Mathematics
Volume	414
DOIs	https://doi.org/10.1016/j.aim.2023.108864
State	Published - Feb 1 2023

Bibliographical note

Funding Information:
KH supported by NSF Grants DMS-1406564 and DMS-1549147 .

Publisher Copyright:
© 2023

Keywords

Contact homology
Contact structure
Reeb dynamics
Symplectic field theory

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10.1016/j.aim.2023.108864

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title = "Semi-global Kuranishi charts and the definition of contact homology",

abstract = "We define the contact homology algebra for any contact manifold and show that it is an invariant of the contact manifold. More precisely, given a contact manifold (M,ξ) and some auxiliary data D, we define an algebra HC(D). If D1 and D2 are two choices of auxiliary data for (M,ξ), then HC(D1) and HC(D2) are isomorphic. We use a simplified version of Kuranishi perturbation theory, consisting of semi-global Kuranishi charts.",

keywords = "Contact homology, Contact structure, Reeb dynamics, Symplectic field theory",

author = "Erkao Bao and Ko Honda",

note = "Funding Information: KH supported by NSF Grants DMS-1406564 and DMS-1549147 . Publisher Copyright: {\textcopyright} 2023",

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AU - Honda, Ko

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N2 - We define the contact homology algebra for any contact manifold and show that it is an invariant of the contact manifold. More precisely, given a contact manifold (M,ξ) and some auxiliary data D, we define an algebra HC(D). If D1 and D2 are two choices of auxiliary data for (M,ξ), then HC(D1) and HC(D2) are isomorphic. We use a simplified version of Kuranishi perturbation theory, consisting of semi-global Kuranishi charts.

AB - We define the contact homology algebra for any contact manifold and show that it is an invariant of the contact manifold. More precisely, given a contact manifold (M,ξ) and some auxiliary data D, we define an algebra HC(D). If D1 and D2 are two choices of auxiliary data for (M,ξ), then HC(D1) and HC(D2) are isomorphic. We use a simplified version of Kuranishi perturbation theory, consisting of semi-global Kuranishi charts.

KW - Contact homology

KW - Contact structure

KW - Reeb dynamics

KW - Symplectic field theory

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JO - Advances in Mathematics

JF - Advances in Mathematics

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ER -

Semi-global Kuranishi charts and the definition of contact homology

Abstract

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