Fundamental theorems of Morse theory on posets-Reference-Cited by-同舟云学术

Fundamental theorems of Morse theory on posets

Published:2022 Issue:8 Volume:7 Page:14922-14945
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Fernández-Ternero D.¹,Macías-Virgós E.²,Mosquera-Lois D.²,Scoville N. A.³,Vilches J. A.¹

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference31 articles.

1. P. Alexandroff, Diskrete Räume, Rec. Math. Moscou, n. Ser., 2 (1937), 501–519.

2. T. F. Banchoff, Critical points and curvature for embedded polyhedra, J. Differ. Geom., 1 (1967), 245–256. https://doi.org/10.4310/jdg/1214428092

3. T. F. Banchoff, Critical points and curvature for embedded polyhedra. Ⅱ. Differential geometry (College Park, Md., 1981/1982), 34–55, Progr. Math., 32, Birkhäuser Boston, Boston, MA, 1983.

4. J. A. Barmak, Algebraic topology of finite topological spaces and applications, Lecture Notes in Mathematics 2032, Springer, Heidelberg, 2011.

5. J. A Barmak, E. G. Minian, One-point reductions of finite spaces, $h$-regular CW-complexes and collapsibility, Algebr. Geom. Topol., 8 (2008), 1763–1780. https://doi.org/10.2140/agt.2008.8.1763

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