Robert Ernest Gompf (born 1957) is an American mathematician specializing in

geometric topology In mathematics, geometric topology is the study of manifolds and Map (mathematics)#Maps as functions, maps between them, particularly embeddings of one manifold into another. History Geometric topology as an area distinct from algebraic topo ...

. Gompf received a Ph.D. in 1984 from the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

under the supervision of

Robion Kirby Robion Cromwell Kirby (born February 25, 1938) is a Professor of Mathematics at the University of California, Berkeley who specializes in low-dimensional topology. Together with Laurent C. Siebenmann he developed the Kirby–Siebenmann invariant ...

(''An invariant for Casson handles, disks and knot concordants''). He is now a professor at the

University of Texas The University of Texas at Austin (UT Austin, UT, or Texas) is a public research university in Austin, Texas, United States. Founded in 1883, it is the flagship institution of the University of Texas System. With 53,082 students as of fall 2 ...

at Austin. His research concerns the topology of

4-manifold In mathematics, a 4-manifold is a 4-dimensional topological manifold. A smooth 4-manifold is a 4-manifold with a smooth structure. In dimension four, in marked contrast with lower dimensions, topological and smooth manifolds are quite different. T ...

s. In 1990, he demonstrated with Tomasz Mrowka that there is a simply connected irreducible 4-manifold that admits no complex structures. In 1995, he constructed new examples of simply connected compact symplectic 4-manifolds that are not homeomorphic or diffeomorphic to complex manifolds (

Kähler manifold In mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure. The concept was first studied by Jan Arnol ...

s). He is a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. He was an

invited speaker at the International Congress of Mathematicians An invitation system is a method of encouraging people to join an organization, such as a Club (organization), club or a website. In regular society, it refers to any system whereby new members are chosen; they cannot simply apply. In relation to w ...

in 1994 in Zurich (''Smooth four-manifolds and symplectic topology'').

Writings

*With András I. Stipsicz: ''4-manifolds and Kirby calculus'', AMS 1999 *''A new construction of symplectic manifolds'', Annals of Mathematics, Volume 142, 1995, p. 527–595 *With Tomasz Mrowka ''Irreducible four manifolds need not be complex'', Annals of Mathematics, Volume 138, 1993, p. 61–111 *''Handlebody construction of Stein surfaces'', Annals of Mathematics, Volume 148, 1998, p. 619–693

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1957 births Living people 20th-century American mathematicians 21st-century American mathematicians Fellows of the American Mathematical Society {{US-mathematician-stub