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