Fundamental theorems of Morse theory on posets

D. Fernández-Ternero; E. Macías-Virgós; D. Mosquera-Lois; N. A. Scoville; J. A. Vilches; D. Fernández-Ternero; E. Macías-Virgós; D. Mosquera-Lois; N. A. Scoville; J. A. Vilches

doi:10.3934/math.2022818

AIMS Mathematics

2022, Volume 7, Issue 8: 14922-14945. doi: 10.3934/math.2022818

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Research article

Fundamental theorems of Morse theory on posets

1.
Departamento de Geometría y Topología, Universidad de Sevilla, Spain
2.
CITMAga, Universidade de Santiago de Compostela, Spain
3.
Department of Mathematics and Computer Science, Ursinus College, Collegeville PA 19426 U.S.A

Received: 27 March 2022 Revised: 24 May 2022 Accepted: 26 May 2022 Published: 13 June 2022
MSC : 06A07, 37B35, 55U99

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.
- Morse theory,
- finite spaces,
- posets,
- two-wide posets,
- down-wide posets
Citation: D. Fernández-Ternero, E. Macías-Virgós, D. Mosquera-Lois, N. A. Scoville, J. A. Vilches. Fundamental theorems of Morse theory on posets[J]. AIMS Mathematics, 2022, 7(8): 14922-14945. doi: 10.3934/math.2022818

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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.

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