Geodesic
Topology of Almost Complex Structures on Six-Manifolds
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the space of (orthogonal) almost complex structures on closed six-dimensional manifolds as the space of sections of the twistor space for a given metric. For a connected six-manifold with vanishing first Betti number, we express the space of almost complex structures as a quotient of the space of sections of a seven-sphere bundle over the manifold by a circle action, and then use this description to compute the rational homotopy theoretic minimal model of the components that satisfy a certain Chern number condition. We further obtain a formula for the homological intersection number of two sections of the twistor space in terms of the Chern classes of the corresponding almost complex structures.
Keywords: almost complex structure, twistor space, space of almost complex structures. 
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     author = {Gustavo Granja and Aleksandar Milivojevi\'c},
     title = {Topology of {Almost} {Complex} {Structures} on {Six-Manifolds}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a92/}
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Gustavo Granja; Aleksandar Milivojević. Topology of Almost Complex Structures on Six-Manifolds. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a92/

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