One-relator Kaehler groups

Abstract

We prove that a one-relator group $G$ is Kähler if and only if either $G$ is finite cyclic or $G$ is isomorphic to the fundamental group of a compact orbifold Riemann surface of genus $g>0$ with at most one cone point of order $n$: $$<a_1{b}_1...a_g{b}_g\mid (\prod _{i=1}^g[a_i{b}_i]{)}^n>.$$

v2: 9pgs. no figs. Final version, to appear in "Geometry and Topology"

References in corpus (1)

• Intersections of conjugates of Magnus subgroups of one-relator groups

Cited by in corpus (3)

• Coxeter groups and Kähler groups
• Quasiprojective three-manifold groups and complexification of three-manifolds
• Restrictions on the prime to $p$ fundamental group of a smooth projective variety