The question in the title, first raised by Goldman and Donaldson, was partially answered by Reznikov. We give a complete answer, as follows: if can be realized as both the fundamental group of a closed 3-manifold and of a compact Kähler manifold, then must be finite—and thus belongs to the well-known list of finite subgroups of , acting freely on .
A Wirtinger presentation of a knot group is obtained from a diagram of the knot. T. Yajima showed that for a 2-knot or a closed oriented surface embedded in the Euclidean 4-space, a Wirtinger presentation of the knot group is obtained from a diagram in an analogous way. J. S. Carter and M. Saito generalized the method to non-orientable surfaces in 4-space by cutting non-orientable sheets of their diagrams by some arcs. We give a modification to their method so that one does not need to find and...