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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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:

a1,b1,,ag,bg|( i=1g[a i,bi])n.

Keywords
Kähler group, one-relator group, orbifold
Mathematical Subject Classification 2010
Primary: 32Q15, 57M05, 57M50
Secondary: 14F35, 32J15
References
Publication
Received: 3 February 2012
Revised: 30 April 2012
Accepted: 3 August 2012
Published: 10 January 2013
Proposed: Benson Farb
Seconded: Ronald Stern, David Gabai
Authors
Indranil Biswas
School of Mathematics
Tata Institute of Fundamental Research
Homi Bhabha Road
Bombay 400005
India
Mahan Mj
Department of Mathematics
RKM Vivekananda University
P.O. Belur Math, Dt Howrah
Howrah 711202
India
http://maths.rkmvu.ac.in/~mahan/