Selman Akbulut

Selman Akbulut Yusuf (* 1949 in Balikesir, Turkey) is a Turkish mathematician who deals with geometric topology.

Akbulut studied at the University of California, Berkeley with a Bachelor 's degree in 1971 and his doctorate in 1975 at Robion Kirby ( Algebraic equations for a class of PL- manifolds ). As a post-doctoral researcher, he in 1975 /76 ( and 1980/81, 2002 and 2005 ) at the Institute for Advanced Study. In 1976 he was Assistant Professor at the University of Wisconsin, 1978 at Rutgers University and in 1981 Assistant Professor, Associate Professor in 1983 and 1986, Professor at Michigan State University.

1982/83 he worked at the Max Planck Institute for Mathematics in Bonn, 1984/85 and several times thereafter at MSRI, 1998 at Feza Gürsey Institute and in 2005 at Harvard University.

Akbulut proved with Henry C. King, that any compact PL- manifold is a real algebraic set, and found new topological invariants with king of real algebraic sets. He focused in particular on low-dimensional manifolds, especially 4 - manifolds. His construction of the Akbulut cork ( first reported in 1988, so called from Kirby ) contains exotic diffeomorphisms structures and is used in counter-examples for the validity of the h- Kobordismen - set of Stephen Smale for smooth manifolds in four dimensions. Akbulut deals with the open smooth Poincaré conjecture in dimension 4 The Poincaré conjecture was indeed proved by Michael Freedman in this dimension, but there still remained the question of whether there is simply connected, closed 4 -manifolds which are homeomorphic to 4- sphere, but are not diffeomorphic (smooth Poincaré conjecture ).

1983 to 1985 he was Sloan Fellow.

Writings

• With HC King: Real algebraic variety structures on PL manifolds, Bulletin of the AMS, Volume 83, 1977, 2
• With HC King: The topology of real algebraic sets with isolated singularities, Annals of Mathematics, Volume 113, 1981, p 425-446
• With HC King: Topology of Real Algebraic Sets, L' Enseignment Math, Volume 29, 1983, pp. 221-261
• With HC King: Topology of Real Algebraic Sets, MSRI Book Series 25, Springer Verlag 1992
• On Representing homology classes of 4 - manifolds, Inventiones Mathematicae, Volume 49, 1978, p 193-198
• A fake compact contractible 4 -manifold, Journ. of Diff. Geom, Volume 33, 1991, pp. 335-356 ( Akbulut corks )
• With K. Yasui: Corks, Plugs and exotic structures, Journal of Gokova Geometry Topology, Volume 2, 2008, pp. 40-82
• A solution to a conjecture of Zeeman, Topology, Volume 30, 1991, pp. 513-515.
• With R. Maveyev: A convex decomposition theorem for 4- manifolds, Int. Math Res Notes, No. 7, 1998, 371-381
• Scharlemann 's manifold is standard, Annals of Mathematics, Volume 149, 1999, pp. 497-510.
• Cappell - Shaneson homotopy spheres are standard, Annals of Mathematics, Volume 171, 2010, pp. 2171-2175.
• Cappell - Shaneson 's 4 - dimensional s- cobordism, Geometry Topology, Volume 6, 2002, pp. 425-494.
• With John D. McCarthy: Casson 's invariant for oriented homology 3- spheres. An exposition, Princeton University Press, 1990