turkmath.org

First I will review the history of Algebraic Realization Problem of Smooth Manifolds starting from Seifert's 1936 result to Tognoli and to Akbulut and King. Then I will introduce some tools typical to the subject like algebraic homology and strongly algebraic vector bundles. Finally, I will present a result (joint with one of my former masters' student Arzu Çelikten) which introduces an obstruction for a topological vector bundle to admit a strongly algebraic structure. Using this obstruction we will construct examples of manifolds promised in the title.