Georges de Rham

painter.^[2] In 1919 he moved with his family to Lausanne in a rented apartment in Beaulieu Castle, where he would live for the rest of his life. Georges de Rham started the Gymnasium in Lausanne with a focus on humanities, following his passion for literature and philosophy but learning little mathematics. On graduating from the Gymnasium in 1921 however, he decided not to continue with the Faculty of Letters in order to avoid Latin. He opted instead for the Faculty of Sciences of the University of Lausanne. At the faculty he started out studying biology, physics and chemistry and no mathematics initially. While trying to learn some mathematics by himself as a tool for physics, his interest was raised and by the third year he abandoned biology to focus decisively on mathematics.^[3]

Joseph Serret. After graduating in 1925, de Rham remained at the University of Lausanne as an assistant to Dumas. Starting work towards completing his doctorate, he read the works of Henri Poincaré on topology on the advice of Dumas. Although he found inspiration for a thesis subject in Poincaré, progress was slow as topology was a relatively new topic and access to the relevant literature was difficult in Lausanne.^[2] With the recommendation of Dumas, de Rham contacted Lebesgue and went to Paris for a few months in 1926 and, again, for a few months in 1928. Both trips were financed by his own savings and he spent his time in Paris taking classes and studying at the University of Paris and the Collège de France. Lebesgue provided de Rham with a lot of help in this period, both with his studies and supporting his first research publications. When he finished his thesis Lebesgue advised him to send it to Élie Cartan and, in 1931, De Rham received his doctorate from the University of Paris before a commission led by Cartan and including Paul Montel and Gaston Julia as examiners.^[1]

Valais; this meeting was the beginning of a more than 40-year friendship between Whitney and de Rham.^[7]

cohomology theory, although he did not do so himself.^[8] In this form, his thesis work has become foundational to the field of differential topology, while his theory of currents is basic to geometric measure theory and related fields.^[10][11] His work is particularly important for Hodge theory and sheaf theory

holonomy groups. In 1952 De Rham considered the converse, proving that, if there is a decomposition of the tangent bundle into vector subbundles which are invariant under the holonomy group, then the Riemannian structure must decompose as a product. This result, now known as the de Rham decomposition theorem, has become a fundamental textbook result in Riemannian geometry.^[12][13]