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De Rham Theory

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Abstract

By the fundamental theorem for line integrals (Theorem 23.13), if a smooth vector field F is the gradient of a scalar function f, then for any two points p and q in \(\mathbb{R}^{3}\), the line integral \(\int_{c}\mathbf{F} \cdot \) d r can be computed in terms of its values at the two endpoints as f (q)- f (p).

Keywords

  • Exact Sequence
  • Differential Form
  • Cohomology Class
  • Homotopy Type
  • Cochain Complex

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  • DOI: 10.1007/978-1-4419-7400-6_8
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Correspondence to Loring W. Tu .

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© 2011 Springer Science+Business Media, LLC

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Tu, L.W. (2011). De Rham Theory. In: An Introduction to Manifolds. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7400-6_8

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