| Georges De Rham |
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| CATEGORIES ABOUT GEORGES DE RHAM | |
| 1903 births | |
| 1990 deaths | |
| swiss mathematicians | |
| 20th century mathematicians | |
| topologists | |
| people from vaud | |
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He studied at the University Of Lausanne and then in Paris for a doctorate, becoming a lecturer in Lausanne in 1931; where he held positions until retirement in 1971; he held positions in Geneva in parallel. In 1931 he proved s the Homology Theory was known to be self-dual with the switch of dimension to codimension (that is, from H''k'' to H''n-k'', where ''n'' is the dimension). That is true, anyway, for Orientable Manifold s, an orientation being in Differential Form terms an ''n''-form that is never zero (and two being equivalent if related by a positive scalar field). The duality can to great advantage be reformulated in terms of the Hodge Dual - intuitively, 'divide into' an orientation form - as it was in the years succeeding the theorem. Separating out the homological and differential form sides allowed the coexistence of 'integrand' and 'domains of integration', as ''cochains'' and ''chains'', with clarity. De Rham himself developed a theory of Homological Current s, that showed how this fitted with the Generalised Function concept. The influence of de Rham’s theorem was particularly great during the development of Hodge Theory and Sheaf theory. De Rham also worked on the Torsion Invariant s of smooth manifolds. SEE ALSO |
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