Geodesic
Toric origami structures on quasitoric manifolds
Informatics and Automation, Geometry, topology, and applications, Tome 288 (2015), pp. 16-37.

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We construct quasitoric manifolds of dimension $6$ and higher which are not equivariantly homeomorphic to any toric origami manifold. All necessary topological definitions and combinatorial constructions are given, and the statement is reformulated in discrete geometrical terms. The problem reduces to the existence of planar triangulations with certain coloring and metric properties. 
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A. A. Aizenberg; M. Masuda; Seonjeong Park; Haozhi Zeng. Toric origami structures on quasitoric manifolds. Informatics and Automation, Geometry, topology, and applications, Tome 288 (2015), pp. 16-37. http://geodesic.mathdoc.fr/item/TRSPY_2015_288_a1/

[1] Ayzenberg A., Buchstaber numbers and classical invariants of simplicial complexes, E-print, 2014, arXiv: 1402.3663 [math.CO]

[2] Ayzenberg A., Masuda M., Park S., Zeng H., Cohomology of toric origami manifolds with acyclic proper faces, E-print, 2014, arXiv: 1407.0764 [math.AT]

[3] Bukhshtaber V.M., Panov T.E., “Kombinatorika simplitsialno kletochnykh kompleksov i toricheskie deistviya”, Tr. MIAN, 247, 2004, 41–58 | MR | Zbl

[4] Buchstaber V.M., Panov T.E., Toric topology, E-print, 2012, arXiv: 1210.2368 [math.AT] | MR

[5] Buchstaber V.M., Panov T.E., Ray N., “Spaces of polytopes and cobordism of quasitoric manifolds”, Moscow Math. J., 7:2 (2007), 219–242 | MR | Zbl

[6] Cannas da Silva A., Guillemin V., Pires A.R., “Symplectic origami”, Int. Math. Res. Not., 2011:18 (2011), 4252–4293, arXiv: 0909.4065 [math.SG] | MR | Zbl

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

[8] Delaunay C., “On hyperbolicity of toric real threefolds”, Int. Math. Res. Not., 2005:51 (2005), 3191–3201 | DOI | MR | Zbl

[9] Delzant T., “Hamiltoniens périodiques et images convexes de l'application moment”, Bull. Soc. math. France., 116 (1988), 315–339 | MR | Zbl

[10] Djidjev H.N., “On the problem of partitioning planar graphs”, SIAM. J. Algebraic Discrete Methods, 3:2 (1982), 229–240 | DOI | MR | Zbl

[11] Erokhovets N., Buchstaber invariant of simple polytopes, E-print, 2009, arXiv: 0908.3407 [math.AT]

[12] Holm T.S., Pires A.R., “The topology of toric origami manifolds”, Math. Res. Lett., 20:5 (2013), 885–906, arXiv: 1211.6435 [math.SG] | DOI | MR | Zbl

[13] Le Gall J.-F., “Large random planar maps and their scaling limits”, Proc. 5th Eur. Congr. Math., Amsterdam, 2008, Eur. Math. Soc., Zürich, 2010, 253–276 | DOI | MR | Zbl

[14] Le Gall J.-F., “Uniqueness and universality of the Brownian map”, Ann. Probab., 41:4 (2013), 2880–2960, arXiv: 1105.4842 [math.PR] | DOI | MR | Zbl

[15] Le Gall J.-F., Paulin F., “Scaling limits of bipartite planar maps are homeomorphic to the 2-sphere”, Geom. Funct. Anal., 18 (2008), 893–918, arXiv: math/0612315 [math.PR] | DOI | MR | Zbl

[16] Lü Z., Panov T., “Moment–angle complexes from simplicial posets”, Cent. Eur. J. Math., 9:4 (2011), 715–730, arXiv: 0912.2219 [math.AT] | DOI | MR | Zbl

[17] Masuda M., Park S., “Toric origami manifolds and multi-fans”, Tr. MIAN, 286, 2013, 331–346, arXiv: 1305.6347 [math.SG]

[18] Oda T., Convex bodies and algebraic geometry: An introduction to the theory of toric varieties, Springer, Berlin, 1988 | MR | Zbl

[19] Osserman R., “The isoperimetric inequality”, Bull. Amer. Math. Soc., 84:6 (1978), 1182–1238 | DOI | MR | Zbl

[20] Yoshida T., “Local torus actions modeled on the standard representation”, Adv. Math., 227:5 (2011), 1914–1955 | DOI | MR | Zbl

[21] Ziegler G.M., Lectures on polytopes, Springer, New York, 2007 | MR