1964 C D Papakyriakopoulos
... for his papers "On Solid Tori", and "On Dehn's lemma and the asphericity of knots".
1964 Raoul Bott
... for his papers "The space of loops on a Lie group", and "The stable homotopy of the classical groups".
1966 Stephen Smale
... for his contributions to various aspects of differential topology.
1966 Morton Brown and Barry Mazur
... for their work on the generalized Schoenflies theorem.
1971 Robion C Kirby
... for his paper "Stable homeomorphisms and the annulus conjecture".
1971 Dennis P Sullivan
... for his work on the Hauptvermutung summarized in the paper "On the Hauptvermutung for manifolds".
1976 William P Thurston
... for his work on foliations.
1976 James Simons
... for his work on minimal varieties and characteristic forms.
1981 Mikhael Gromov
... for his work relating topological and geometric properties of Riemannian manifolds.
1981 Shing-Tung Yau
... for his work in nonlinear partial differential equations, his contributions to the topology of differentiable manifolds, and for his work on the complex Monge-Ampère equation on compact complex manifolds.
1986 Michael H Freedman
... for his work in differential geometry and, in particular, the solution of the four-dimensional Poincaré conjecture.
1991 Andrew J Casson
... for his work on the topology of low-dimensional manifolds, and to Clifford H Taubes for his foundational work in Yang-Mills theory.
1996 Richard Hamilton
... for his continuing study of the Ricci flow and related parabolic equations for a Riemannian metric, and to Gang Tian for his contributions to geometric analysis.
2001 Jeff Cheeger
... for his work in differential geometry, to Yakov Eliashberg for his work in symplectic and contact topology, and to Michael J Hopkins for his work in homotopy theory.
2004 David Gabai
... in recognition of his work in geometric topology, in particular, the topology of 3-dimensional manifolds.
2007 Peter Kronheimer and Tomasz Mrowka
... for their joint contributions to both three- and four-dimensional topology through the development of deep analytical techniques and applications.
2007 Peter Ozsváth and Zoltán Szabó
... for their contributions to 3- and 4-dimensional topology through their Heegaard Floer homology theory.
History of the AMS
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