Morse index of a cyclic polygon

Gaiane Panina; Alena Zhukova

Open Mathematics (2011)

  • Volume: 9, Issue: 2, page 364-377
  • ISSN: 2391-5455

Abstract

top
It is known that cyclic configurations of a planar polygonal linkage are critical points of the signed area function. In the paper we give an explicit formula of the Morse index for the signed area of a cyclic configuration. We show that it depends not only on the combinatorics of a cyclic configuration, but also on its metric properties.

How to cite

top

Gaiane Panina, and Alena Zhukova. "Morse index of a cyclic polygon." Open Mathematics 9.2 (2011): 364-377. <http://eudml.org/doc/269474>.

@article{GaianePanina2011,
abstract = {It is known that cyclic configurations of a planar polygonal linkage are critical points of the signed area function. In the paper we give an explicit formula of the Morse index for the signed area of a cyclic configuration. We show that it depends not only on the combinatorics of a cyclic configuration, but also on its metric properties.},
author = {Gaiane Panina, Alena Zhukova},
journal = {Open Mathematics},
keywords = {Morse index; Linkage; Moduli space; Cyclic polygon; linkage; moduli space; cyclic polygon},
language = {eng},
number = {2},
pages = {364-377},
title = {Morse index of a cyclic polygon},
url = {http://eudml.org/doc/269474},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Gaiane Panina
AU - Alena Zhukova
TI - Morse index of a cyclic polygon
JO - Open Mathematics
PY - 2011
VL - 9
IS - 2
SP - 364
EP - 377
AB - It is known that cyclic configurations of a planar polygonal linkage are critical points of the signed area function. In the paper we give an explicit formula of the Morse index for the signed area of a cyclic configuration. We show that it depends not only on the combinatorics of a cyclic configuration, but also on its metric properties.
LA - eng
KW - Morse index; Linkage; Moduli space; Cyclic polygon; linkage; moduli space; cyclic polygon
UR - http://eudml.org/doc/269474
ER -

References

top
  1. [1] Cerf J., La stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie, Publ. Math. Inst. Hautes Études Sci., 1970, 39, 5–173 http://dx.doi.org/10.1007/BF02684687 Zbl0213.25202
  2. [2] Elerdashvili E., Jibladze M., Khimshiashvili G., Cyclic configurations of pentagon linkages, Bull. Georgian Acad. Sci., 2008, 2(4), 29–32 Zbl1193.52012
  3. [3] Farber M., Schütz, D., Homology of planar polygon spaces, Geom. Dedicata, 2007, 125(1), 75–92. http://dx.doi.org/10.1007/s10711-007-9139-7 Zbl1132.52024
  4. [4] Khimshiashvili G., Configuration spaces and signature formulas, J. Math. Sci. (N. Y.), 2009, 160(6), 727–736 http://dx.doi.org/10.1007/s10958-009-9524-x Zbl1181.14061
  5. [5] Panina G., Khimshiashvili G., Cyclic polygons are critical points of area, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 2008, 360, 238–245 Zbl1193.52015
  6. [6] Pólya G., Mathematics and Plausible Reasoning. Vol. 1: Induction and Analogy in Mathematics, Princeton University Press, Princeton, 1954 
  7. [7] Zvonkine D., Configuration spaces of hinge constructions. Russ. J. Math. Phys., 1997, 5(2), 247–266 Zbl0924.57016

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.