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to GL(''n'', '''C'''). The existence question is then a purely algebraic topological one and is fairly well understood.

Examples

For every integer n, the flat space R²ⁿ admits an almost complex structure. An example for such an almost complex structure is (1 <= j, k <= 2n): for odd j, for even j.

The only spheres which admit almost complex structures are S² and S⁶ . In particular,

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