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- Homological_integration abstract "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 Dk of k-currents on a manifold M is defined as the dual space, in the sense of distributions, of the space of k-forms Ωk on M. Thus there is a pairing between k-currents T and k-forms α, denoted here byUnder this duality pairing, the exterior derivative goes over to a boundary operatordefined byfor all α ∈ Ωk. This is a homological rather than cohomological construction.".
- Homological_integration wikiPageID "23029956".
- Homological_integration wikiPageRevisionID "564115276".
- Homological_integration hasPhotoCollection Homological_integration.
- Homological_integration subject Category:Definitions_of_mathematical_integration.
- Homological_integration subject Category:Measure_theory.
- Homological_integration type Abstraction100002137.
- Homological_integration type Communication100033020.
- Homological_integration type Definition106744396.
- Homological_integration type DefinitionsOfMathematicalIntegration.
- Homological_integration type Explanation106738281.
- Homological_integration type Message106598915.
- Homological_integration type Statement106722453.
- Homological_integration comment "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.".
- Homological_integration label "Homological integration".
- Homological_integration sameAs m.064m9dw.
- Homological_integration sameAs Q5891419.
- Homological_integration sameAs Q5891419.
- Homological_integration sameAs Homological_integration.
- Homological_integration wasDerivedFrom Homological_integration?oldid=564115276.
- Homological_integration isPrimaryTopicOf Homological_integration.