Geodesic
Equivariant Almost Complex Structures on Quasitoric Manifolds
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometry, topology, and mathematical physics. II, Tome 266 (2009), pp. 140-148.

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It is proved that there exists an equivariant almost complex structure on any quasitoric manifold that admits a positive omniorientation. This gives an answer to the question raised by M. Davis and T. Januszkiewicz: Find a criterion for the existence of an equivariant almost complex structure on a quasitoric manifold in terms of its characteristic function. 
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A. A. Kustarev. Equivariant Almost Complex Structures on Quasitoric Manifolds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometry, topology, and mathematical physics. II, Tome 266 (2009), pp. 140-148. http://geodesic.mathdoc.fr/item/TM_2009_266_a7/

[1] Wu W.-T., “Sur les classes caractéristiques des structures fibrées sphériques”, Sur les espaces fibrés et les variétés feuilletées, Actual. sci. et ind., 1183, Hermann, Paris, 1952, 5–89 | MR

[2] Thomas E., “Complex structures on real vector bundles”, Amer. J. Math., 89 (1967), 887–908 | DOI | MR | Zbl

[3] Bredon G., Vvedenie v teoriyu kompaktnykh grupp preobrazovanii, Nauka, M., 1980 | MR | Zbl

[4] Atiyah M. F., “Convexity and commuting Hamiltonians”, Bull. London Math. Soc., 14:1 (1982), 1–15 | DOI | MR | Zbl

[5] Fomenko A. T., Fuks D. B., Kurs gomotopicheskoi topologii, Nauka, M., 1989 | MR

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

[7] Taubes C. H., “The Seiberg–Witten invariants and symplectic forms”, Math. Res. Lett., 1 (1994), 809–822 | DOI | MR | Zbl

[8] Panov T. E., “Rody Khirtsebrukha mnogoobrazii s deistviem tora”, Izv. RAN. Ser. mat., 65:3 (2001), 123–138 | DOI | MR | Zbl

[9] Feldman K. E., Hirzebruch genera of manifolds equipped with a Hamiltonian circle action, E-print , 2001 arXiv: math/0110028v2

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

[11] 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