In 1975 he earned his Ph.D. from the University of California, Berkeley as a student of Robion Kirby. In topology, he has worked on handlebody theory, low-dimensional manifolds, symplectic topology, G2 manifolds. In the topology of real-algebraic sets, he and Henry C. King proved that every compact piecewise-linear manifold is a real-algebraic set; they discovered new topological invariants of real-algebraic sets.
He has developed 4-dimensional handlebody techniques, settling conjectures and solving problems about 4-manifolds, such as Zeeman conjecture, Harer-Kas-Kirby conjecture, Scharlemann problem, and Cappell-Shaneson problems. He constructed an exotic compact 4-manifold (with boundary) from which he discovered "Akbulut corks".
His most recent results concern the 4-dimensional smooth Poincare conjecture. He has supervised 12 Ph.D students as of 2016. He has more than 95 papers and 3 books published, and several books edited.
- S. Akbulut, A solution to a conjecture of Zeeman, Topology, vol.30, no.3, (1991), 513-515.
- S.Akbulut, Scharlemann's manifold is standard, Ann of Math., 149 (1999) 497-510.
- S. Akbulut, Cappell-Shaneson homotopy spheres are standard Ann. of Math., 171 (2010) 2171-2175.
- S.Akbulut, Cappell-Shaneson's 4-dimensional s-cobordism, Geometry-Topology, vol.6, (2002), 425-494.
- M. Freedman, R. Gompf, S. Morrison, K. Walker, Man and machine thinking about the smooth 4-dimensional Poincaré conjecture. Quantum Topol. 1 (2010), no. 2, 171–208
- B. Ozbagci and A.I. Stipsicz. Surgery on contact 3-manifolds and Stein surfaces (p. 14), Springer ISBN 3-540-22944-2
- A.Scorpan, The wild world of 4-manifolds (p.90), AMS Pub. ISBN 0-8218-3749-4
- Institute for Advanced Study: A Community of Scholars
- Selman Akbulut at the Mathematics Genealogy Project
- Akbulut's homepage
- Akbulut's papers at ArXiv
- Akbulut-King invariants
- Real algebraic geometry
- Akbulut cork
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