On invertible generating pairs of fundamental groups of graph manifolds

Mathematics – Geometric Topology

Scientific paper

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

Scientific paper

10.2140/gtm.2008.14.105

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.

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