Topology of Almost Complex Structures on Six-Manifolds
Differential Geometry
2022-12-05 v2 Algebraic Topology
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.
Keywords
Cite
@article{arxiv.2207.12946,
title = {Topology of Almost Complex Structures on Six-Manifolds},
author = {Gustavo Granja and Aleksandar Milivojević},
journal= {arXiv preprint arXiv:2207.12946},
year = {2022}
}