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arXiv · 2207.12946

Topology of Almost Complex Structures on Six-Manifolds

Gustavo Granja·Aleksandar Milivojević
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Abstract

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.

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Gustavo Granja, Aleksandar Milivojević. 2022-07-26. Topology of Almost Complex Structures on Six-Manifolds. https://doi.org/10.3842/sigma.2022.093

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