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In the mathematical fields of differential geometry and geometric measure theory, homological integration or geometric integration is a method for extending the notion of the integral to manifolds. Rather than functions or differential forms, the integral is defined over currents on a manifold. The theory is "homological" because currents themselves are defined by duality with differential forms. To wit, the space ''D''''k'' of ''k''-currents on a manifold ''M'' is defined as the dual space, in the sense of distributions, of the space of ''k''-forms Ω''k'' on ''M''. Thus there is a pairing between ''k''-currents ''T'' and ''k''-forms α, denoted here by : Under this duality pairing, the exterior derivative : goes over to a boundary operator : defined by : for all α ∈ Ω''k''. This is a homological rather than cohomological construction. ==References== * * . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Homological integration」の詳細全文を読む スポンサード リンク
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