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On invertible generating pairs of fundamental groups of
graph manifolds
Michel Boileau and Richard Weidmann |
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Geometry & Topology Monographs 14 (2008) 105–128 |
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arXiv: 0904.1380 |
Abstract |
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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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Dedicated to Heiner Zieschang, our teacher, mentor and friend |
KeywordsHeegaard genus, rank, involutions of 3–manifolds, graph manifolds |
Mathematical Subject ClassificationPrimary: 20F34 Secondary: 57M27 |
References |
PublicationReceived: 21 October 2006 |
Authors |
| Michel Boileau | |
| Laboratoire Émile Picard CNRS UMR 5580 Université Paul Sabatier 118 Route de Narbonne F-31062 Toulouse Cedex 4 France |
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| Richard Weidmann | |
| Department of Mathematics and the
Maxwell Institute of Mathematical Sciences Heriot-Watt University Riccarton Edinburgh EH14 4AS Scotland |
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