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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     author = {A. A. Kustarev},
     title = {Equivariant {Almost} {Complex} {Structures} on {Quasitoric} {Manifolds}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     url = {http://geodesic.mathdoc.fr/item/TM_2009_266_a7/}
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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/