On invertible generating pairs of fundamental groups of graph manifolds

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.

This is the version published by Geometry & Topology Monographs on 29 April 2008