Volume 16, issue 4 (2012)

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One-relator Kähler groups

Indranil Biswas and Mahan Mj

Geometry & Topology 16 (2012) 2171–2186
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 $n$:

$〈{a}_{1},{b}_{1},\dots ,{a}_{g},{b}_{g}|{\left(\prod _{i=1}^{g}\left[{a}_{i},{b}_{i}\right]\right)}^{\phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}n}〉.$

Keywords
Kähler group, one-relator group, orbifold
Mathematical Subject Classification 2010
Primary: 32Q15, 57M05, 57M50
Secondary: 14F35, 32J15