Geodesic
Geometric presentation for the cohomology ring of polygon spaces
Algebra i analiz, Tome 31 (2019) no. 1, pp. 80-91.

Voir la notice de l'article provenant de la source Math-Net.Ru

We describe the cohomology ring of the moduli space of a flexible polygon in geometrically meaningful terms. We propose two presentations, both are computation friendly: there are simple rules for the cup product.
Keywords: polygonal linkage, Chern class, Euler class, intersection theory, moduli space. 
@article{AA_2019_31_1_a3,
     author = {I. Nekrasov and G. Panina},
     title = {Geometric presentation for the cohomology ring of polygon spaces},
     journal = {Algebra i analiz},
     pages = {80--91},
     publisher = {mathdoc},
     volume = {31},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AA_2019_31_1_a3/}
}
TY  - JOUR
AU  - I. Nekrasov
AU  - G. Panina
TI  - Geometric presentation for the cohomology ring of polygon spaces
JO  - Algebra i analiz
PY  - 2019
SP  - 80
EP  - 91
VL  - 31
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2019_31_1_a3/
LA  - en
ID  - AA_2019_31_1_a3
ER  - 
%0 Journal Article
%A I. Nekrasov
%A G. Panina
%T Geometric presentation for the cohomology ring of polygon spaces
%J Algebra i analiz
%D 2019
%P 80-91
%V 31
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2019_31_1_a3/
%G en
%F AA_2019_31_1_a3
I. Nekrasov; G. Panina. Geometric presentation for the cohomology ring of polygon spaces. Algebra i analiz, Tome 31 (2019) no. 1, pp. 80-91. http://geodesic.mathdoc.fr/item/AA_2019_31_1_a3/

[1] Agapito J., Godinho L., “Intersection numbers of polygon spaces”, Trans. Amer. Math. Soc., 361:9 (2009), 4969–4997 | DOI | MR | Zbl

[2] Kamiyama Y., “A polynomial with coefficients in certain elementary symmetric polynomials”, JP J. Algebra Number Theory Appl., 39:3 (2017), 389–399 | DOI | Zbl

[3] Klyachko A., “Spatial polygons and stable configurations of points in the projective line”, Algebraic Geometry and its Appl. (Yaroslavl', 1992), Aspects Math., 25, Friedr. Vieweg, Braunschweig, 1994, 67–84 | DOI | MR

[4] Kontsevich M., “Intersection theory on the moduli space of curves and the matrix Airy function”, Comm. Math. Phys., 147:1 (1992), 1–23 | DOI | MR | Zbl

[5] Nekrasov I., Panina G., Zhukova A., Intersection numbers of Chern classes of tautological line bundles on the moduli spaces of flexible polygons, arXiv: 1707.04144

[6] Hausmann J.-C., Knutson A., “The cohomology ring of polygon spaces”, Ann. Inst. Fourier, 48:1 (1998), 281–321 | DOI | MR | Zbl