AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home AIMS Mathematics Article
PDF (324.6 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

Fundamental theorems of Morse theory on posets

D. Fernández-Ternero1, E. Macías-Virgós2( ), D. Mosquera-Lois2, N. A. Scoville3, J. A. Vilches1
Departamento de Geometría y Topología, Universidad de Sevilla, Spain
CITMAga, Universidade de Santiago de Compostela, Spain
Department of Mathematics and Computer Science, Ursinus College, Collegeville PA 19426 U.S.A
Show Author Information

Abstract

We prove a version of the fundamental theorems of Morse theory in the setting of finite partially ordered sets. By using these results we extend Forman's discrete Morse theory to more general cell complexes and derive the Morse-Pitcher inequalities in that context.

Keywords

Morse theoryfinite spacesposetstwo-wide posetsdown-wide posets
CLC number: 06A07, 37B35, 55U99

References

【1】
【1】
 
 
Crossref Google Scholar
AIMS Mathematics
Volume 7 Issue 8,
August 2022
Pages 14922-14945
DOI: 10.3934/math.2022818

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
Fernández-Ternero D, Macías-Virgós E, Mosquera-Lois D, et al. Fundamental theorems of Morse theory on posets. AIMS Mathematics, 2022, 7(8): 14922-14945. https://doi.org/10.3934/math.2022818

10

Views

0

Downloads

0

Crossref

0

Web of Science

0

Scopus
Received: 27 March 2022
Revised: 24 May 2022
Accepted: 26 May 2022
Published: 15 August 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)