Richard Swan

Richard Gordon Swan ( born December 21, 1933, New York City ) is an American mathematician who (among other things with algebraic K-theory ) deals with algebra.

Swan was Putnam Fellow in 1952 and studied at Princeton University, where he earned his doctorate under John Coleman Moore, 1957 ( Spaces with finite groups of transformations ). He was a professor at the University of Chicago.

He is known for the Swan -Serre theorem (or Swan theorem), which establishes a connection (via functoriality of categories) between topology and algebra. It expresses an equivalence of vector bundles on compact spaces with finitely generated projective modules over commutative rings, and had been previously suspected by Jean -Pierre Serre.

His doctoral counts Charles Weibel. In 1970 he was invited speaker at the International Congress of Mathematicians in Nice ( Algebraic -theory ). In 1970 he received the Cole prize for his work in algebra Groups of cohomological dimension one (Journal of Algebra Bd.12, 1969, S.585 ). In it he showed that free groups are characterized in that their cohomological dimension 1 ( previously shown in a special case of John Stallings, co- recipient of the prize was Cole ).

In 1970 he gave a plenary lecture at the ICM in Nice ( Algebraic K- Theory). He is a member of the National Academy of Sciences.

Writings

• The theory of sheaves. University of Chicago Press 1964.
• Algebraic - Theory. Lecture Notes in Mathematics, Springer 1968.
• Vector bundles and projective modules. Trans Amer. Math Society, Vol. 105, 1962, p.264 - 277th