De Rham–Weil theorem

In algebraic topology, the De Rham–Weil theorem allows computation of sheaf cohomology using an acyclic resolution of the sheaf in question.

Let be a sheaf on a topological space and a resolution of by acyclic sheaves. Then

where denotes the -th sheaf cohomology group of with coefficients in

The De Rham–Weil theorem follows from the more general fact that derived functors may be computed using acyclic resolutions instead of simply injective resolutions.

References

  • Rham, Georges De (1931). "Sur l'analysis situs des variétés à n dimensions - Tome (1931) no. 129". {{cite journal}}: Cite journal requires |journal= (help)
  • Samelson, Hans (1967). "On de Rham's theorem". Topology. 6 (4): 427–432. doi:10.1016/0040-9383(67)90002-X.
  • Well, André (1952). "Sur les théorèmes de de Rham". Commentarii Mathematici Helvetici. 26: 119–145. doi:10.1007/BF02564296. S2CID 124799328.

This article incorporates material from De Rham–Weil theorem on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.