Robion Kirby

Robion Cromwell Kirby (born February 25, 1938) is a Professor of Mathematics at the University of California, Berkeley who specializes in low-dimensional topology. Together with Laurent C. Siebenmann he invented the Kirby–Siebenmann invariant for classifying the piecewise linear structures on a topological manifold. He also proved the fundamental result on the Kirby calculus, a method for describing 3-manifolds and smooth 4-manifolds by surgery on framed links. Along with his significant mathematical contributions, he is an influential figure in the field, with over 50 doctoral students and his famous problem list.

Robion Kirby
Robion Kirby.jpeg
Robion Kirby in Berkeley
Born (1938-02-25) February 25, 1938 (age 82)
NationalityUnited States
Alma materUniversity of Chicago
Known forKirby–Siebenmann class
Kirby calculus
AwardsOswald Veblen Prize in Geometry (1971)
NAS Award for Scientific Reviewing (1995)
Scientific career
InstitutionsUniversity of California, Berkeley
Doctoral advisorEldon Dyer[1]
Doctoral students

He received his Ph.D. from the University of Chicago in 1965. He soon became an assistant professor at UCLA. While there he developed his "torus trick" which enabled him to solve, in dimensions greater than four (with additional joint work with Siebenmann), four of John Milnor's seven most important problems in geometric topology.[2]

In 1971, he was awarded the Oswald Veblen Prize in Geometry by the American Mathematical Society.

In 1995 he became the first mathematician to receive the NAS Award for Scientific Reviewing from the National Academy of Sciences for his problem list in low-dimensional topology.[3] He was elected to the National Academy of Sciences in 2001. In 2012 he became a fellow of the American Mathematical Society.[4]

Kirby is also the President of Mathematical Sciences Publishers, a small non-profit academic publishing house that focuses on mathematics and engineering journals.


  • Kirby, Robion C.; Siebenmann, Laurence C. (1977). Foundational Essays on Topological Manifolds, Smoothings, and Triangulations (PDF). Annals of Mathematics Studies. 88. Princeton, NJ: Princeton University Press. ISBN 0-691-08191-3. MR 0645390.
  • Kirby, Robion C. (1989). The topology of 4-manifolds. Lecture Notes in Mathematics. 1374. Berlin, New York: Springer-Verlag. doi:10.1007/BFb0089031. ISBN 978-3-540-51148-9. MR 1001966.[5]


  1. ^ Robion Kirby at the Mathematics Genealogy Project
  2. ^ S. Ferrry. Lecture notes in geometric topology (PDF).
  3. ^ "NAS Award for Scientific Reviewing". National Academy of Sciences. Archived from the original on 18 March 2011. Retrieved 27 February 2011.
  4. ^ List of Fellows of the American Mathematical Society, retrieved 2013-01-27.
  5. ^ Taylor, Lawrence R. (1991). "Review: Robion C. Kirby, The topology of 4 manifolds". Bull. Amer. Math. Soc. (N.S.). 24 (2): 466–471. doi:10.1090/s0273-0979-1991-16068-4.

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