CONTACT HOMOLOGY AND HIGHER DIMENSIONAL CLOSING LEMMAS

Julian Chaidez; Ipsita Datta; Rohil Prasad; Shira Tanny

doi:10.3934/jmd.2024003

CONTACT HOMOLOGY AND HIGHER DIMENSIONAL CLOSING LEMMAS

Julian Chaidez
, Ipsita Datta
, Rohil Prasad
, Shira Tanny

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

3 Scopus citations

Abstract

We develop methods for studying the smooth closing lemma for Reeb flows in any dimension using contact homology. As an application, we prove a conjecture of Irie, stating that the strong closing lemma holds for Reeb flows on ellipsoids. Our methods also apply to other Reeb flows, and we illustrate this for a class of examples introduced by Albers–Geiges–Zehmisch.

Original language	English (US)
Pages (from-to)	67-153
Number of pages	87
Journal	Journal of Modern Dynamics
Volume	20
DOIs	https://doi.org/10.3934/jmd.2024003
State	Published - 2024
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Applied Mathematics

Keywords

closing lemma
contact topology
periodic orbits
Reeb dynamics

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10.3934/jmd.2024003

Cite this

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title = "CONTACT HOMOLOGY AND HIGHER DIMENSIONAL CLOSING LEMMAS",

abstract = "We develop methods for studying the smooth closing lemma for Reeb flows in any dimension using contact homology. As an application, we prove a conjecture of Irie, stating that the strong closing lemma holds for Reeb flows on ellipsoids. Our methods also apply to other Reeb flows, and we illustrate this for a class of examples introduced by Albers–Geiges–Zehmisch.",

keywords = "closing lemma, contact topology, periodic orbits, Reeb dynamics",

author = "Julian Chaidez and Ipsita Datta and Rohil Prasad and Shira Tanny",

year = "2024",

doi = "10.3934/jmd.2024003",

language = "English (US)",

volume = "20",

pages = "67--153",

journal = "Journal of Modern Dynamics",

issn = "1930-5311",

publisher = "American Institute of Mathematical Sciences",

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TY - JOUR

T1 - CONTACT HOMOLOGY AND HIGHER DIMENSIONAL CLOSING LEMMAS

AU - Chaidez, Julian

AU - Datta, Ipsita

AU - Prasad, Rohil

AU - Tanny, Shira

PY - 2024

Y1 - 2024

N2 - We develop methods for studying the smooth closing lemma for Reeb flows in any dimension using contact homology. As an application, we prove a conjecture of Irie, stating that the strong closing lemma holds for Reeb flows on ellipsoids. Our methods also apply to other Reeb flows, and we illustrate this for a class of examples introduced by Albers–Geiges–Zehmisch.

AB - We develop methods for studying the smooth closing lemma for Reeb flows in any dimension using contact homology. As an application, we prove a conjecture of Irie, stating that the strong closing lemma holds for Reeb flows on ellipsoids. Our methods also apply to other Reeb flows, and we illustrate this for a class of examples introduced by Albers–Geiges–Zehmisch.

KW - closing lemma

KW - contact topology

KW - periodic orbits

KW - Reeb dynamics

UR - https://www.scopus.com/pages/publications/85190393984

UR - https://www.scopus.com/pages/publications/85190393984#tab=citedBy

U2 - 10.3934/jmd.2024003

DO - 10.3934/jmd.2024003

M3 - Article

AN - SCOPUS:85190393984

SN - 1930-5311

VL - 20

SP - 67

EP - 153

JO - Journal of Modern Dynamics

JF - Journal of Modern Dynamics

ER -

CONTACT HOMOLOGY AND HIGHER DIMENSIONAL CLOSING LEMMAS

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

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