by Finnur LÃ¡russon
Abstract: We introduce the four classes of complex manifolds defined by having "few" or "many" holomorphic maps to or from the complex plane. Two of these classes have played an important role in complex geometry for a long time. A third turns out to be too large to be of much interest. The fourth class has only recently emerged from work of Mikhail Gromov. These are the so-called Oka manifolds that were formally defined only a few months ago. We will motivate the definition of an Oka manifold, sketch what is known about them, and mention two major applications of the ambient theory.
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