The theory of characteristic classes began in the year 1935 with almost simultaneous work by HASSLER WHITNEY in the United States and EDUARD STIEFEL in Switzerland. Stiefel’s thesis, written under the direction of Heinz Hopf, introduce and studied certain “characteristic” homology classes determined by the tangent bundle of a smooth manifold. Whitney, then at Harvard University, treated the case of an arbitrary sphere bundle. Somewhat later he invented the language of cohomology theory, hence the concept of a characteristic cohomology class, and proved the basic product theorem.
In 1942 LEV PONTRJAGIN of Moscow University began to study the homology of Grassmann manifolds, using a cell subdivision due to Charles Ehresmann. This enabled him to construct important new characteristic classes. (Pontrjagin’s many contributions to mathematics are the more remarkable in that he is totally blind, having lost his eyesight in an accident at the age of fourteen.)
In 1946 SHING-SHEN CHERN, recently arrived at the Institute for Advanced Study from Kunming in southwestern China, defined classes for complex vector bundles. In fact he showed that the complex Grassmann manifolds have a cohomology structure which is much easier to understand than that of the real Grassmann manifolds.
According to this site, E. Stiefel
was awarded his doctorate for his thesis Richtungsfelder und Fernparallelismus in n-dimensionalen Mannigfaltigkeiten from ETH Zürich in 1935. He published the results of this thesis in a paper in 1936.
the 1936., is of course Stiefel’s paper on Stiefel-Whitney characteristic classes.
That sites quotes
who say in the paper
… perhaps Stiefel’s most famous contribution to pure mathematics, was dedicated to a fundamental study of the theory of vector fields on manifolds. Generalising the classical notion of the Eulerian characteristic of a manifold, he introduced the idea of the characteristic classes.
In that paper,
page 324, “Characteristik” (number) seems to appear for the first time:
Die Zahl a heisst due Characteristik des -Feldes auf der Sphaere .
Pontrjagin’s 1942 paper is