The Work of Samuel Eilenberg in Topology

Abstract

This chapter focuses on the work of Samuel Eilenberg in topology. Algebraic topology is growing and solving problems, but non-topologists are very skeptical. At Harvard, Tucker gave an expert on cell complexes and their homology. In Poland, Kuratowski led a very vigorous school, with notable results flowing from his students. In a paper on Extension and Classification of Continuous Mappings at the 1940 Conference on Topology at the University of Michigan, Sammy formulated in explicit, clear, and easily usable form all the essential properties of obstructions to the extension of continuous maps, codifying effective but vague ideas then in the air. This paper is a fine example of Sammy's influence and style—the same style is also exhibited in his 1944 paper on Singular Homology, in which he carved out the clear and direct definition of the singular complex.