Deane Montgomery (2 September 1909 – 15 March 1992) was an American mathematician specializing in topology who was one of the contributors to the final resolution of Hilbert's fifth problem in the 1950s. He served as President of the American Mathematical Society from 1961 to 1962.
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- THEOREM: if G is a locally euclidean, connected, simply connected topological group of dimension n greater than one, then G contains a closed proper subgroup of positive dimension.
- A group which has a simple structure may offer difficult questions when operating as a transformation group. For example, the ways in which a cyclic group of order 2 can operate on a manifold, even on E 3, are far from completely known.
- "Properties of finite-dimensional groups". Proceedings of the International Mathematical Congress held in Cambridge, Mass. in 1950. University of Toronto Press. 1952. pp. 442–446. (quote from p. 442)
Quotes about Deane Montgomery
- Others have spoken and written about his solution of Hilbert's fifth problem, but perhaps not enough is said about his later work, especially his joint work with C. T. Yang. In a long series of papers written in the late 1960s and early 1970s, they used the study of group actions on homotopy 7-spheres to showcase and test the growing new techniques of differential topology, especially index theory and surgery theory. At a time when much work in topology consisted in building these machines, their papers demonstrated the beauty of applying this theory to unfurl complexities of symmetry and structure.
- Ronald Fintushel in: (March 2005)"A Tribute to Deane Montgomery". Notices of the AMS 52 (3): 348–349. (quote from p. 349)