One-relator Kaehler groups

Details One-relator Kaehler groups One-relator Kaehler groups

2012-01-27

arxiv.org/abs/1201.5772v1

Mathematics

Geometric Topology

8pgs. no figs

Scientific paper

We prove that a one-relator group $G$ is K\"ahler 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
$n$: $$< a_1\, b_1\, \,...\, a_g\, b_g\, \mid\, (\prod_{i=1}^g [a_i\,
b_i])^n>\, .$$

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