In the mathematical field of geometric topology, the Poincaré conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space.
Sergei Petrovich Novikov is a Soviet and Russian mathematician, noted for work in both algebraic topology and soliton theory. In 1970, he won the Fields Medal.
Michael Hartley Freedman is an American mathematician, at Microsoft Station Q, a research group at the University of California, Santa Barbara. In 1986, he was awarded a Fields Medal for his work on the 4-dimensional generalized Poincaré conjecture. Freedman and Robion Kirby showed that an exotic ℝ4 manifold exists.
Sir Simon Kirwan Donaldson is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähler geometry. He is currently a permanent member of the Simons Center for Geometry and Physics at Stony Brook University in New York, and a Professor in Pure Mathematics at Imperial College London.
Nigel James Hitchin FRS is a British mathematician working in the fields of differential geometry, gauge theory, algebraic geometry, and mathematical physics. He is a Professor Emeritus of Mathematics at the University of Oxford.
Jeffrey Renwick Weeks is an American mathematician, a geometric topologist and cosmologist. Weeks is a 1999 MacArthur Fellow.
In topology, a branch of mathematics, a topological manifold is a topological space that locally resembles real n-dimensional Euclidean space. Topological manifolds are an important class of topological spaces, with applications throughout mathematics. All manifolds are topological manifolds by definition. Other types of manifolds are formed by adding structure to a topological manifold. Every manifold has an "underlying" topological manifold, obtained by simply "forgetting" the added structure. However, not every topological manifold can be endowed with a particular additional structure. For example, the E8 manifold is a topological manifold which cannot be endowed with a differentiable structure.
Dusa McDuff FRS CorrFRSE is an English mathematician who works on symplectic geometry. She was the first recipient of the Ruth Lyttle Satter Prize in Mathematics, was a Noether Lecturer, and is a Fellow of the Royal Society. She is currently the Helen Lyttle Kimmel '42 Professor of Mathematics at Barnard College.
Dennis Parnell Sullivan is an American mathematician known for his work in algebraic topology, geometric topology, and dynamical systems. He holds the Albert Einstein Chair at the City University of New York Graduate Center and is a distinguished professor at Stony Brook University.
In mathematics, a 5-manifold is a 5-dimensional topological manifold, possibly with a piecewise linear or smooth structure.
John Willard Morgan is an American mathematician known for his contributions to topology and geometry. He is a Professor Emeritus at Columbia University and a member of the Simons Center for Geometry and Physics at Stony Brook University.
William Bernard Raymond Lickorish is a mathematician. He is emeritus professor of geometric topology in the Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, and also an emeritus fellow of Pembroke College, Cambridge. His research interests include topology and knot theory. He was one of the discoverers of the HOMFLY polynomial invariant of links, and proved the Lickorish-Wallace theorem which states that all closed orientable 3-manifolds can be obtained by Dehn surgery on a link.
John Robert Stallings Jr. was a mathematician known for his seminal contributions to geometric group theory and 3-manifold topology. Stallings was a Professor Emeritus in the Department of Mathematics at the University of California at Berkeley where he had been a faculty member since 1967. He published over 50 papers, predominantly in the areas of geometric group theory and the topology of 3-manifolds. Stallings' most important contributions include a proof, in a 1960 paper, of the Poincaré Conjecture in dimensions greater than six and a proof, in a 1971 paper, of the Stallings theorem about ends of groups.
James W. Cannon is an American mathematician working in the areas of low-dimensional topology and geometric group theory. He was an Orson Pratt Professor of Mathematics at Brigham Young University.
Herbert Blaine Lawson, Jr. is a mathematician best known for his work in minimal surfaces, calibrated geometry, and algebraic cycles. He is currently a Distinguished Professor of Mathematics at Stony Brook University. He received his PhD from Stanford University in 1969 for work carried out under the supervision of Robert Osserman.
Yakov Matveevich Eliashberg is an American mathematician who was born in Leningrad, USSR.
Danny Matthew Cornelius Calegari is a mathematician who is currently a professor of mathematics at the University of Chicago. His research interests include geometry, dynamical systems, low-dimensional topology, and geometric group theory.
Ralph Louis Cohen is an American mathematician, specializing in algebraic topology and differential topology.
Paul Alexander Schweitzer, S. J., is an American mathematician, specializing in differential topology, geometric topology, and algebraic topology.
Ivan Smith is a British mathematician who deals with symplectic manifolds and their interaction with algebraic geometry, low-dimensional topology, and dynamics. He is a professor at the University of Cambridge.
