wptmath.cornell.edu

Professor at the Department of Mathematics, Cornell University, Ithaca, NY, USA.

Topology

Pr Thurston has revolutionized the study of topology in 2 and 3 dimensions, showing interplay between analysis, topology, and geometry. He contributed the idea that a very large class of closed 3-manifolds carry a hyperbolic structure.

Bill Thurston is a topologist, though his work impinges on many other areas of mathematics. He has discovered unexpected links between topology, hyperbolic geometry, and complex analysis.

Highlights of his career include his classification of foliations of codimension greater than one, his classification of surface automorphisms, his hyperbolization theorem in three-dimensional topology, and the theories of automatic groups and confoliations. Thurston has also made fundamental contributions to the theory of symplectic and contact manifolds, dynamics of surface diffeomorphisms, and the combinatorics of rational maps.

His current research includes random 3-manifolds and relations of knot theory to computational complexity. His main interest remains his geometrization conjecture, a far-reaching proposed generalization of his hyperpolization theorem.

1982 Fields Medal.

Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. (N.S.) 6 (1982), 357–381.

Hyperbolic structures on 3-manifolds, I. Deformation of acylindrical manifolds, Ann. of Math. 124 (1986), 203–246.

Word Processing in Groups (with D. B. A. Epstein, J. W. Cannon, D. F. Holt, S. V. F. Levy, and M. S. Paterson), Jones and Bartlet Publishers, Boston, MA, 1992.

Three-Dimensional Geometry and Topology, Princeton Mathematical Series 35, Princeton University Press, Princeton, NJ, 1997.

Confoliations (with Y. Eliashberg), AMS, Providence, RI, 1998.

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