Richard Swan

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


Swan was a Putnam Fellow in 1952 and studied at Princeton University , where he received his PhD under John Coleman Moore in 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 via commutative rings and was previously suspected by Jean-Pierre Serre .

Charles Weibel is one of his doctoral students .

In 1970 he was invited speaker at the International Congress of Mathematicians (ICM) in Nice and held the plenary lecture Algebraic -theory . In 1970 he received the Cole Prize in Algebra for his work Groups of cohomological dimension one (Journal of Algebra Vol. 12, 1969, p. 585). In it he showed that free groups are characterized by the fact that their cohomological dimension is 1 (previously shown in a special case by John Stallings , who was a co-recipient of the Cole Prize).

In 1961 he became a Sloan Research Fellow . He has been a member of the National Academy of Sciences since 1976 .


  • 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, pp. 264-277.

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