Richard Swan

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Richard Gordon Swan (/swɑːn/; born 1933) is an American mathematician who is known for the Serre–Swan theorem relating the geometric notion of vector bundles to the algebraic concept of projective modules,[1] and for the Swan representation, an l-adic projective representation of a Galois group.[2] His work has mainly been in the area of algebraic K-theory.

Education and career[edit]

Swan earned his Ph.D. in 1957 from Princeton University under the supervision of John Coleman Moore.[3] In 1969 he proved in full generality what is now known as the Stallings-Swan theorem.[4][5] He is the Louis Block Professor Emeritus of Mathematics at the University of Chicago.[6] His doctoral students at Chicago include Charles Weibel, also known for his work in K-theory.[3]


  • Swan, R. G. (1964). The Theory of Sheaves. Chicago lectures in mathematics. Chicago: The University of Chicago Press.
  • Swan, R. G. (1968). Algebraic K-theory. Lecture Notes in Mathematics. 76. Berlin, New York: Springer-Verlag. doi:10.1007/BFb0080281. ISBN 978-3-540-04245-7. MR 0245634.
  • Swan, Richard G. (1970). K-theory of finite groups and orders. Lecture Notes in Mathematics. 149. Notes by E. Graham Evans. Berlin, New York: Springer-Verlag. doi:10.1007/BFb0059150. ISBN 978-3-540-04938-8. MR 0308195.


  1. ^ Manoharan, P. (1995), "Generalized Swan's Theorem and its Application", Proceedings of the American Mathematical Society, 123 (10): 3219–3223, doi:10.2307/2160685, JSTOR 2160685.
  2. ^ Huber, R. (2001), "Swan representations associated with rigid analytic curves", Journal für die Reine und Angewandte Mathematik, 537 (537): 165–234, doi:10.1515/crll.2001.063, MR 1856262.
  3. ^ a b Richard Gordon Swan at the Mathematics Genealogy Project
  4. ^ Weigel, Thomas; Zalesskii, Pavel (2016). "Virtually free pro-p products". arXiv:1305.4887 [math.GR].
  5. ^ Swan, R. G. (1969). "Groups of cohomological dimension one". Journal of Algebra. 12 (4): 585–610. doi:10.1016/0021-8693(69)90030-1.
  6. ^ University of Chicago Mathematics Faculty Listing, retrieved 2015-08-31.

External links[edit]