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ISSN (electronic): 1464-8997
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On invertible generating pairs of fundamental groups of graph manifolds

Michel Boileau and Richard Weidmann

Geometry & Topology Monographs 14 (2008) 105–128

DOI: 10.2140/gtm.2008.14.105

arXiv: 0904.1380

Abstract

We study invertible generating pairs of fundamental groups of graph manifolds, that is, pairs of elements (g,h) for which the map g → g-1, h → h-1 extends to an automorphism. We show in particular that a graph manifold is of Heegaard genus 2 if and only if its fundamental group has an invertible generating pair.

Dedicated to Heiner Zieschang, our teacher, mentor and friend

Keywords

Heegaard genus, rank, involutions of 3–manifolds, graph manifolds

Mathematical Subject Classification

Primary: 20F34

Secondary: 57M27

References
Publication

Received: 21 October 2006
Accepted: 5 February 2007
Published: 29 April 2008

Authors
Michel Boileau
Laboratoire Émile Picard
CNRS UMR 5580
Université Paul Sabatier
118 Route de Narbonne
F-31062 Toulouse Cedex 4
France
Richard Weidmann
Department of Mathematics and the Maxwell Institute of Mathematical Sciences
Heriot-Watt University
Riccarton
Edinburgh
EH14 4AS
Scotland