Deane Montgomery

thumb|Deane Montgomery 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. Quotes 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 theorem on locally euclidean groups Annals of Mathematics 1947 650–658 10.2307/1969132 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 442–446 University of Toronto Press 1952 http://www.mathunion.org/ICM/ICM1950.2/Main/icm1950.2.0442.0446.ocr.pdf (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: A Tribute to Deane Montgomery Notices of the AMS March 2005 52 3 348–349 http://www.ams.org/notices/200503/comm-fintushel.pdf (quote from p. 349) External links Category:1992 deaths Category:Mathematicians from the United States Category:People from Minnesota Category:Members of the American Philosophical Society Category:Guggenheim Fellows