Chercheurs

Mathématiques / GABAI, DAVID

gabai

Position

Chair, Hughes-Rogers Professor of Mathematics, Department of Mathematics, Princeton University, USA.

Thèmes de recherche

Low-dimensional topology/geometry, knot theory, foliations, hyperbolic geometry

Intensely focused on low-dimensional topology and hyperbolic geometry, he is a leading researcher in those subjects.

Prix et récompenses

NSF Graduate Fellowship 1976
NSF Postdoctoral Fellowship 1980
Sloan Foundation Fellowship 1986
AMS Centennial Fellowship 1988
Oswald Veblen Prize in Geometry 2004
Clay Research Award 2009
Hughes-Rogers Professor 2009-
National Academy of Sciences 2011
Fellow of the American Mathematical Society 2012

Publications

The Murasugi Sum is a Natural Geometric Operation, Contemporary Mathematics 20 (1983), 131-145.

Foliations and the Topology of 3-Manifolds, Bull. AMS 8 (1983), 77-80.

Foliations and the Topology of 3-Manifolds, J. of Diff. Geom. 18 (1983), 445-503.

Foliations and Genera of Links, Topology 23 (1984), 381-394.

The Murasugi Sum is a Natural Geometric Operation II, Contemporary Mathematics 44 (1985), 93-100.

The Simple Loop Conjecture, J. of Diff. Geom. 21 (1985), 143-149.

An Internal Hierarchy for 3-Manifolds, Lecture Notes in Mathematics, Springer 1144 (1985), 14-17.

Genera of the Arborescent Links, Memoirs of the AMS, number 339, 1986.

The Classification of Maps of Surfaces (with Will Kazez), Bull. AMS. 14 (1986), 283-286.

Foliations and Surgery on Knots, Bull. AMS. 15 (1986), 83-87.

Genera of the Alternating Links, Duke Math. J. 53 (1986), 677-681.

Detecting Fibred Links in S3\\\\\\\\\\\\\\\", Commentarii Math. Helvetici, 61 (1986), 519-555.

On 3-Manifolds Covered by Surface Bundles, London Math. Soc. Lecture Notes #112 (1987) 145-156.

Foliations and the Topology of 3-Manifolds II, J. of Diff. Geom. 26 (1987) 461-478.

Foliations and the Topology of 3-Manifolds III, J. of Diff. Geom. 26 (1987) 479-536.

Genus is Superadditive under Band Connected Sum, Topology 26 (1987) 209-210.

The Classification of Maps of Surfaces (with Will Kazez), Invent. Math. 90 (1987) 219-242.

The Classification of Maps of Non Orientable Surfaces (with Will Kazez), Math. Annalen 281 (1988) 687-702.

Surgery on Knots in Solid Tori, Topology 28 (1989), 1-6.

Essential Laminations in 3-Manifolds (with Ulrich Oertel), Annals of Math. 130 (1989) 41-73.

Pseudo Anosov Maps and Surgery on Fibred 2-Bridge Knots (with Will Kazez), Topology and its Applications 37 (1990), 93-100.

1-Bridge Braids in Solid Tori, Topology and its Applications 37 (1990), 221-235.

Convergence Groups are Fuchsian Groups, Bull. AMS (2) 25 (1991), 395-402.

3-Manifolds and Foliations, Proc. Int. Cong. Math. 1990 Kyoto (1992), 609-619.

Taut Foliations of 3-Manifolds and Suspensions of S1, Ann. Inst. Fourier 42 (1992), 193-208.

Convergence Groups are Fuchsian Groups, Annals of Math. 136 (1992), 447-510.

3-Manifolds with Essential Laminations are Covered by Solid Tori (with Will Kazez), J. Lon. Math. Soc. (2) 47 (1993), 557-576.

Homotopy Hyperbolic 3-Manifolds are Virtually Hyperbolic, JAMS 7 (1994), 193-198.

On the Geometric and Topological Rigidity of Hyperbolic 3-Manifolds, Bull. AMS 31 (1994), 228-232.

Valentin Poenaru\\\\\\\\\\\\\\\'s Program for the Poincaré Conjecture, Geom. Top. Physics. for Raoul Bott, Int. Press., (1995), 139-166.

Homotopy, Isotopy and Genuine Laminations of 3-Manifolds (with Will Kazez), Proc. 1993 Georgia Top. Conf., Stud. in Adv. Math. Vol 2.1, (1997), 123-138.

Problems on the Geometric Theory of Foliations and Laminations on 3-Manifolds, Proc. 1993 Georgia Top. Conf., Stud. in Adv. Math. Vol 2.2, (1997), 1-34.

On the Geometric and Topological Rigidity of Hyperbolic 3-Manifolds, JAMS 10 (1997), 37-74.

Order trees and laminations of the plane (with Will Kazez), Math. Res. Letters 4 (1997), 603-616.

Group Negative Curvature for 3-Manifolds with Genuine Laminations (with Will Kazez), Geom. and Top. 2 (1998) 65-77.

Semi-Euclidean Laminations in 3-Manifolds, Surveys in Differential Geometry (Inter. Press) 3 (1998) 195-242.

Finiteness of the Mapping Class Group for 3-Manfolds with Essential Laminations, (with Will Kazez), J. Diff. Geom. 50 (1998), 123-127.

On Brittenham’s Theorem, to appear in Comm. in Analysis and Geometry.

Taut Foliations and Combinatorial Volume Preserving Flows, Comm. Math. Helv. 75 (2000), 109-124.

3 Lectures on Foliations and Laminations on 3-Manifolds, to appear in Proc. 1998 SUNY, Stony Brook, Laminations Conference.

Homotopy Hyperbolic 3-Manifolds are Hyperbolic (with Robert Meyerhoff, Nathaniel Thurston), to appear in Annals of Math.

Essential Laminations and Kneser Normal Form, to appear in J. Diff. Geom.

Volumes of Tubes in Hyperbolic 3-Manifolds (with Robert Meyerhoff, Peter Milley), preprint.

The Smale Conjecture for Hyperbolic 3-Manifolds: Isom(M 3)\\\\\\\\\\\\\\\\simeq Diff(M 3), preprint