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Dennis Sullivan
Dennis Parnell Sullivan (born February 12, 1941〔.〕) is an American mathematician. He is known for work in topology, both algebraic and geometric, and on dynamical systems. He holds the Albert Einstein Chair at the City University of New York Graduate Center, and is a professor at Stony Brook University.
==Work in topology==
He received his B.A. in 1963 from Rice University and his doctorate in 1966 from Princeton University. His Ph.D. thesis, entitled ''Triangulating homotopy equivalences'', was written under the supervision of William Browder, and was a contribution to surgery theory. He was a permanent member of the Institut des Hautes Études Scientifiques from 1974 to 1997.
Sullivan is one of the founders of the surgery method of classifying high-dimensional manifolds, along with Browder, Sergei Novikov and C. T. C. Wall. In homotopy theory, Sullivan put forward the radical concept that spaces could directly be ''localised'', a procedure hitherto applied to the algebraic constructs made from them. He founded (along with Daniel Quillen) rational homotopy theory.
The Sullivan conjecture, proved in its original form by Haynes Miller, states that the classifying space ''BG'' of a finite group ''G'' is sufficiently different from any finite CW complex ''X'', that it maps to such an ''X'' only 'with difficulty'; in a more formal statement, the space of all mappings ''BG'' to ''X'', as pointed spaces and given the compact-open topology, is weakly contractible. This area has generated considerable further research. (Both these matters are discussed in his (1970 MIT notes ).)
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