Eilenberg, Samuel (1913- )

Polish-born US mathematician whose research in the field of algebraic topology led to considerable development in the theory of cohomology. Eilenberg was born and educated in Warsaw. In the 1930s he emigrated to the USA. He was professor of mathematics at the University of Indiana 1946-49, and ended his career at Columbia University, New York. Algebraic topology, sometimes called 'combinatorial' topology, is based on homology theory - the study of closed curves, closed surfaces, and similar geometric arrangements in a given topological space. Much of Eilenberg's work was concerned with a modification of homology theory called cohomology theory. It is possible to define a 'product' of cohomology classes by means of which, together with the addition of cohomology classes, the direct sum of the cohomology classes of all dimensions becomes a ring (the cohomology ring). This is a richer structure than is available for homology groups, and allows finer results. Various very complicated algebraic operations using cohomology classes can lead to results not provable in any other way.