Geodesic
Computation of the first Stiefel–Whitney class for the variety $\overline{\mathcal M_{0,n}^\mathbb R}$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 6, pp. 51-75 
N. Ya. Amburg; E. M. Kreines. Computation of the first Stiefel–Whitney class for the variety $\overline{\mathcal M_{0,n}^\mathbb R}$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 6, pp. 51-75. http://geodesic.mathdoc.fr/item/FPM_2013_18_6_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We compute the class $W_{n-4}(\overline{\mathcal M_{0,n}^\mathbb R})$, which is Poincaré dual to the first Stiefel–Whitney class for the variety $\overline{\mathcal M_{0,n}^\mathbb R}$ in terms of the natural cell decomposition of $\overline{\mathcal M_{0,n}^\mathbb R}$.

[1] Ceyhan O., On moduli of pointed real curves of genus zero, 2007, arXiv: math.AG/0207058 | MR

[2] Deligne P., Mumford D., “The irreducibility of the spece of curves of given genus”, Inst. Hautes Études Sci. Publ. Math., 36 (1969), 75–109 | DOI | MR | Zbl

[3] Devadoss S., “Tessellations of moduli spaces and the mosaic operad”, Contemp. Math., 239 (1999), 91–114 | DOI | MR | Zbl

[4] Etingof P., Henriques A., Kamnitzer J., Rains E., “The cohomology ring of the real locus of the moduli space of stable curves of genus $0$ with marked points”, Ann. Math., 171:2 (2010), 731–777 ; arXiv: math.AT/0507514 | DOI | MR | Zbl

[5] Halperin S., Toledo D., “Stiefel–Whitney homology classes”, Ann. Math., 96 (1972), 511–525 | DOI | MR | Zbl

[6] Kapranov M., “The permuto-associahedron, MacLane coherence theorem and the asymptotic zones for the KZ equation”, J. Pure Appl. Agebra, 85 (1993), 119–142 | DOI | MR | Zbl

[7] Keel S., “Intersection theory of moduli space of stable $n$-pointed curves of genus zero”, Trans. Am. Math. Soc., 330:2 (1992), 545–574 | MR | Zbl

[8] Milnor J. W., Stasheff J. D., Characteristic Classes, Ann. Math. Stud., 76, Princeton Univ. Press, Princeton, 1974 | MR | Zbl

[9] Morava J., Braids, trees, and operads, 2001, arXiv: math.AT/0109086