Fundamental theorems of Morse theory on posets

AIMS Mathematics

article

D. Fernández-Ternero¹  E. Macías-Virgós²  D. Mosquera-Lois²  N. A. Scoville³  J. A. Vilches¹ 

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

关键词: Morse theory;    finite spaces;    posets;    two-wide posets;    down-wide posets;   

DOI  :  10.3934/math.2022818

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

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.

【 授权许可】

CC BY