Geodesic
Quasitoric manifolds and small covers over properly coloured polytopes: immersions and embeddings
Sbornik. Mathematics, Tome 207 (2016) no. 4, pp. 479-489 Cet article a éte moissonné depuis la source Math-Net.Ru

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We construct small covers and quasitoric manifolds over $n$-dimensional simple polytopes which allow proper colourings of facets with $n$ colours. We calculate the Stiefel-Whitney classes of these manifolds as obstructions to immersions and embeddings into Euclidean spaces. The largest dimension required for embedding is achieved in the case $n$ is a power of two. Bibliography: 11 titles.
Keywords: embeddings, quasitoric manifolds, simple polytopes, colourings, Stiefel-Whitney classes. 
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D. Baralić; V. Grujić. Quasitoric manifolds and small covers over properly coloured polytopes: immersions and embeddings. Sbornik. Mathematics, Tome 207 (2016) no. 4, pp. 479-489. http://geodesic.mathdoc.fr/item/SM_2016_207_4_a0/

[1] G. M. Ziegler, Lectures on polytopes, Grad. Texts in Math., 152, Springer-Verlag, New York, 1995, x+370 pp. | DOI | MR | Zbl

[2] V. M. Bukhshtaber, T. E. Panov, Toricheskie deistviya v topologii i kombinatorike, MTsNMO, M., 2004, 272 pp. | MR | Zbl

[3] M. Joswig, “Projectivities in simplicial complexes and colorings of simple polytopes”, Math. Z., 240:2 (2002), 243–259 | DOI | MR | Zbl

[4] M. W. Davis, T. Januszkiewicz, “Convex polytopes, Coxeter orbifolds and torus actions”, Duke Math. J., 62:2 (1991), 417–451 | DOI | MR | Zbl

[5] J. W. Milnor, J. D. Stasheff, Characteristic classes, Ann. of Math. Stud., 76, Princeton Univ. Press, Princeton, NJ; Univ. of Tokyo Press, Tokyo, 1974, vii+331 pp. | MR | MR | Zbl | Zbl

[6] M. Ghomi, S. Tabachnikov, “Totally skew embeddings of manifolds”, Math. Z., 258:3 (2008), 499–512 | DOI | MR | Zbl

[7] D. Baralić, B. Prvulović, G. Stojanović, S. Vrećica, R. Živaljević, “Topological obstructions to totally skew embeddings”, Trans. Amer. Math. Soc., 364:4 (2012), 2213–2226 | DOI | MR | Zbl

[8] D. Baralić, “Immersions and embeddings of quasitoric manifolds over the cube”, Publ. Inst. Math. (Beograd) (N.S.), 95:109 (2014), 63–71 | DOI | MR

[9] R. L. Cohen, “The immersion conjecture for differentiable manifolds”, Ann. of Math. (2), 122:2 (1985), 237–328 | DOI | MR | Zbl

[10] W. S. Massey, “On the Stiefel–Whitney classes of a manifold”, Amer. J. Math., 82:1 (1960), 92–102 | DOI | MR | Zbl

[11] W. S. Massey, “Normal vector fields on manifolds”, Proc. Amer. Math. Soc., 12 (1961), 33–40 | DOI | MR | Zbl