Georges de Rham (10 September 1903 – 9 October 1990) was a Swiss mathematician, known for his contributions to differential topology. Events 506 - The Bishops of Visigothic Gaul meet in the Council of Agde. Year 1903 ( MCMIII) was a Common year starting on Thursday (link will display calendar of the Gregorian calendar or a Common year starting Events 768 - Carloman I and Charlemagne are crowned Kings of The Franks. Year 1990 ( MCMXC) was a Common year starting on Monday (link displays the 1990 Gregorian calendar) Switzerland (English pronunciation; Schweiz Swiss German: Schwyz or Schwiiz Suisse Svizzera Svizra officially the Swiss Confederation A mathematician is a person whose primary area of study and research is the field of Mathematics. In Mathematics, differential topology is the field dealing with differentiable functions on Differentiable manifolds It is closely related to Differential
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. The University of Lausanne (in French: Université de Lausanne) or UNIL in Lausanne, Switzerland was founded in 1537 as a school of The historic University of Paris (Université de Paris first appeared in the second half of the 13th century The University of Geneva (Université de Genève is a university in Geneva, Switzerland.
In 1931 he proved de Rham's theorem, identifying the de Rham cohomology groups as topological invariants. In Mathematics, de Rham cohomology (after Georges de Rham) is a tool belonging both to Algebraic topology and to Differential topology, capable In Mathematics, de Rham cohomology (after Georges de Rham) is a tool belonging both to Algebraic topology and to Differential topology, capable This proof can be considered as sought-after, since the result was implicit in the points of view of Henri Poincaré and Élie Cartan. Jules Henri Poincaré ( 29 April 1854 &ndash 17 July 1912) (ˈʒyl ɑ̃ˈʁi pwɛ̃kaˈʁe was a French Mathematician Élie Joseph Cartan ( 9 April 1869 &ndash 6 May 1951) was an influential French Mathematician, who did fundamental The first proof of the general Stokes' theorem, for example, is attributed to Poincaré, in 1899. In Differential geometry, Stokes' theorem is a statement about the integration of Differential forms which generalizes several Theorems from At the time there was no cohomology theory, one could reasonably say: for manifolds the homology theory was known to be self-dual with the switch of dimension to codimension (that is, from Hk to Hn-k, where n is the dimension). In Mathematics, specifically in Algebraic topology, cohomology is a general term for a Sequence of Abelian groups defined from a Cochain A manifold is a mathematical space in which every point has a neighborhood which resembles Euclidean space, but in which the global structure may be In Mathematics, homology theory is the Axiomatic study of the intuitive geometric idea of homology of cycles on Topological spaces It can be broadly That is true, anyway, for orientable manifolds, 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). A surface S in the Euclidean space R 3 is orientable if a two-dimensional figure (for example) cannot be moved around the surface and back In the mathematical fields of Differential geometry and Tensor calculus, differential forms are an approach to Multivariable calculus which is 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. In Mathematics, the Hodge star operator or Hodge dual is a significant Linear map introduced in general by W 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 currents, that showed how this fitted with the generalised function concept. In Mathematics, more particularly in Functional analysis, Differential topology, and Geometric measure theory, a current in the sense of In Mathematics, generalized functions are objects generalizing the notion of functions There is more than one recognised theory
The influence of de Rham’s theorem was particularly great during the development of Hodge theory and sheaf theory. In Mathematics, Hodge theory is one aspect of the study of the Algebraic topology of a Smooth manifold M. In Mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the Open sets of a Topological space.
De Rham also worked on the torsion invariants of smooth manifolds. In mathematics Reidermeister torsion (or R-torsion, or Reidemeister-Franz torsion) is a topological invariant of manifolds introduced by for 3-manifolds and generalized
See also
External links
- O'Connor, John J. In Mathematics, a de Rham curve is a certain type of Fractal Curve. & Robertson, Edmund F. , “Georges de Rham”, MacTutor History of Mathematics archive
- Georges de Rham at the Mathematics Genealogy Project
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