Geodesic
Discrete Morse theory for the barycentric subdivision
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVIII, Tome 462 (2017), pp. 52-64 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Let $F$ be a discrete Morse function on a simplicial complex $L$. We construct a discrete Morse function $\Delta(F)$ on the barycentric subdivision $\Delta(L)$. The constructed function $\Delta(F)$ “behaves the same way” as $F$, i.e., has the same number of critical simplices and the same gradient path structure. 
@article{ZNSL_2017_462_a2,
     author = {A. Zhukova},
     title = {Discrete {Morse} theory for the barycentric subdivision},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {52--64},
     year = {2017},
     volume = {462},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_462_a2/}
}
TY  - JOUR
AU  - A. Zhukova
TI  - Discrete Morse theory for the barycentric subdivision
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2017
SP  - 52
EP  - 64
VL  - 462
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2017_462_a2/
LA  - en
ID  - ZNSL_2017_462_a2
ER  - 
%0 Journal Article
%A A. Zhukova
%T Discrete Morse theory for the barycentric subdivision
%J Zapiski Nauchnykh Seminarov POMI
%D 2017
%P 52-64
%V 462
%U http://geodesic.mathdoc.fr/item/ZNSL_2017_462_a2/
%G en
%F ZNSL_2017_462_a2
A. Zhukova. Discrete Morse theory for the barycentric subdivision. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVIII, Tome 462 (2017), pp. 52-64. http://geodesic.mathdoc.fr/item/ZNSL_2017_462_a2/

[1] R. Forman, “Morse theory for cell complexes”, Adv. Math., 134 (1998), 90–145 | DOI | MR | Zbl

[2] E. Gallais, “Combinatorial realization of the Thom–Smale complex via discrete Morse theory”, Ann. Sc. Norm. Super. Pisa Cl. Sci., 9:2 (2010), 229–252 | MR | Zbl

[3] B. Benedetti, “Smoothing discrete Morse theory”, Ann. Sc. Norm. Super. Pisa Cl. Sc., 16:2 (2016), 335–368 | MR | Zbl

[4] E. Babson, P. Hersh, “Discrete Morse functions from lexicographic orders”, Trans. Amer. Math. Soc., 357:2 (2005), 509–534 | DOI | MR | Zbl