Robion Kirby
Robion Cromwell Kirby ( born February 25, 1938 in Chicago) is an American mathematician who deals with low-dimensional topology.
Life and work
Kirby made 1959 a bachelor's degree in 1960 and his master's degree in 1965 from the University of Chicago doctorate in S. Eldon Dyer ( Smoothing locally flat imbeddings ). After that, he was from 1965 to 1969 assistant professor at the University of California, Los Angeles. He is since 1971 professor of mathematics at the University of California, Berkeley.
With Laurent Siebenmann he is the discoverer of the Kirby - Siebenmann invariants in the classification of PL structures of topological manifolds. These have exactly then a PL structure if a class disappears in the fourth cohomology group of the manifold ( the Kirby - Siebenmann class). Furthermore, the PL- structures are classified by elements of the third cohomology. He developed the Kirby calculus for describing three - and four-dimensional topological manifolds with Surgery ( dissection, surgery ) of framed tangles ( " framed links").
It is also known its list of open problems in low-dimensional topology ( he received even the price for the reviews of the National Academy of Sciences). Kirby ( and Siebenmann ) itself had achieved with their work in the early 1970s, four out of seven issues in 1963 looked at the leading topologist John Milnor as the hardest unsolved problems of geometric topology.
In 1971 he was awarded the Oswald Veblen - Prize of the American Mathematical Society, of which he is a Fellow. In 1974 he was Guggenheim Fellow. He was inducted into the National Academy of Sciences, the NAS Award for Scientific Reviewing he had received in 1995, 2001. In 1970 he was invited speaker at the International Congress of Mathematicians in Nice ( Some conjectures about four- manifolds ).
His doctoral include Tomasz Mrowka, Selman Akbulut and Robert Gompf.
Writings
- Topology of Four - Manifolds. Lecture Notes in Mathematics, Springer-Verlag, 1989.
- With Laurence Taylor: A survey of 4- manifolds through the eyes of surgery. In 1998.
- Kirby, Siebenmann: Foundational Essays on Topological Manifolds, Smoothing Hing, and triangulation. Annals of Mathematical Studies, Princeton 1977, pdf - file.