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**Robert Ernest Gompf** (born 1957) is an American mathematician specializing in geometric topology.

Gompf received a Ph.D. in 1984 from the University of California, Berkeley under the supervision of Robion Kirby (*An invariant for Casson handles, disks and knot concordants*).^{[1]} He is now a professor at the University of Texas at Austin.

His research concerns the topology of 4-manifolds. 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 manifolds).

He is a fellow of the American Mathematical Society.^{[2]} He was an invited speaker at the International Congress of Mathematicians in 1994 in Zurich (*Smooth four-manifolds and symplectic topology*).

- 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

**^**Robert Gompf at the Mathematics Genealogy Project**^**"List of Fellows of the American Mathematical Society". Retrieved February 23, 2014.

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