Discrete Morse theory for the moduli spaces of polygonal linkages, or solitaire on a circle
Sbornik. Mathematics, Tome 208 (2017) no. 9, pp. 1353-1367 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We construct an exact discrete Morse function on the moduli space of a planar polygonal linkage. A cellular structure on the moduli space is used, and the number of cells is minimised by employing discrete Morse theory. Bibliography: 12 entries.
Keywords: polygonal linkage, cell complex, discrete vector field, exact Morse function.
Mots-clés : configuration space
@article{SM_2017_208_9_a4,
     author = {A. M. Zhukova and G. Yu. Panina},
     title = {Discrete {Morse} theory for the moduli spaces of polygonal linkages, or solitaire on a~circle},
     journal = {Sbornik. Mathematics},
     pages = {1353--1367},
     year = {2017},
     volume = {208},
     number = {9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2017_208_9_a4/}
}
TY  - JOUR
AU  - A. M. Zhukova
AU  - G. Yu. Panina
TI  - Discrete Morse theory for the moduli spaces of polygonal linkages, or solitaire on a circle
JO  - Sbornik. Mathematics
PY  - 2017
SP  - 1353
EP  - 1367
VL  - 208
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/SM_2017_208_9_a4/
LA  - en
ID  - SM_2017_208_9_a4
ER  - 
%0 Journal Article
%A A. M. Zhukova
%A G. Yu. Panina
%T Discrete Morse theory for the moduli spaces of polygonal linkages, or solitaire on a circle
%J Sbornik. Mathematics
%D 2017
%P 1353-1367
%V 208
%N 9
%U http://geodesic.mathdoc.fr/item/SM_2017_208_9_a4/
%G en
%F SM_2017_208_9_a4
A. M. Zhukova; G. Yu. Panina. Discrete Morse theory for the moduli spaces of polygonal linkages, or solitaire on a circle. Sbornik. Mathematics, Tome 208 (2017) no. 9, pp. 1353-1367. http://geodesic.mathdoc.fr/item/SM_2017_208_9_a4/

[1] M. Joswig, M. E. Pfetsch, “Computing optimal Morse matchings”, SIAM J. Discrete Math., 20:1 (2006), 11–25 | DOI | MR | Zbl

[2] B. A. Burton, T. Lewiner, J. Paixão, J. Spreer, “Parameterized complexity of discrete Morse theory”, Computational geometry (SoCG'13), ACM, New York, 2013, 127–136 | DOI | MR | Zbl

[3] G. Panina, Moduli space of a planar polygonal linkage: a combinatorial description, arXiv: 1209.3241

[4] J. Milnor, Lectures on the $h$-cobordism theorem, Princeton Univ. Press, Princeton, NJ, 1965, v+116 pp. | MR | Zbl

[5] P. Hersh, “On optimizing discrete Morse functions”, Adv. in Appl. Math., 35:3 (2005), 294–322 | DOI | MR | Zbl

[6] M. Farber, D. Schütz, “Homology of planar polygon spaces”, Geom. Dedicata, 125 (2007), 75–92 | DOI | MR | Zbl

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

[8] M. Farber, Invitation to topological robotics, Zur. Lect. Adv. Math., Eur. Math. Soc., Zürich, 2008, x+133 pp. | DOI | MR | Zbl

[9] M. Farber, J.-C. Hausmann, D. Schütz, “On the conjecture of Kevin Walker”, J. Topol. Anal., 1:1 (2009), 65–86 | DOI | MR | Zbl

[10] G. Yu. Panina, G. N. Khimshiashvili, “On the area of a polygonal linkage”, Dokl. Math., 85:1 (2012), 120–121 | DOI | MR | Zbl

[11] R. Forman, “A user's guide to discrete Morse theory”, Sém. Lothar. Combin., 48 (2002), B48c, 35 pp. | MR | Zbl

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