Kählerian three-manifold groups

Abstract

Abstract. We prove that if the fundamental group of an arbitrary three-manifoldnot necessarily closed, nor orientable -is a Kähler group, then it is either finite or the fundamental group of a closed orientable surface.

Quasiprojective Three-Manifold Groups and Complexification of Three-Manifolds

“…As a consequence of our results we deduce the restrictions on quasiprojective 3-manifold groups obtained by the authors of [DPS,FrSu,Ko2] and the restrictions on good complexifications of 3-manifolds deduced in [To] (this is done in in Section 3.1.1). We also indicate, in Remark 3.12, how to deduce the classification of (closed) 3-manifold Kähler groups [DiSu,Ko1,BMS] using the techniques of Theorem 1.1, thus providing a unified treatment of known results.…”

“…A group is called quasiprojective (respectively, Kähler) if it is the fundamental group of a smooth complex quasiprojective variety (respectively, compact Kähler manifold). Kähler and quasiprojective 3manifold groups have attracted much attention of late [DiSu,Ko1,BMS,DPS,FrSu,Ko2]. In this paper we characterize quasiprojective 3-manifold groups.…”

Kähler groups, quasi-projective groups and 3-manifold groups

“…For instance, if Σ g is a Riemann surface of genus g 2, then π 1 (Σ g × [0, 1]) is certainly a Kähler group. (Added in proof: motivated by Theorem 1.1, and the implicit question we raised here, Kotschick [28] has now shown that, in fact, the only infinite, 3-manifold groups which are also Kähler groups are the surface groups. )…”

Complements to ample divisors and Singularities

“…to be a fundamental group of a smooth quasi-projective variety. For application of these and ideas from different ideas, not discussed here, to the problem of characterisation of quias-projective and quasi-Kahler groups (in particular the comparison with the fundamental groups of 3-manifolds) see: [133], [76], [77], [19], [10], [124], [91], [32] 3.6. Isolated non-normal crossings.…”