Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-05T03:25:24.304Z Has data issue: false hasContentIssue false
  • English
  • Français

Virtual surface Bundle groups

Published online by Cambridge University Press:  17 April 2009

J. A. Hillman
J. A. Hillman
Affiliation:
School of Mathematics and Statistics, The University of Sydney, Sydney NSW 2006, Australia e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that all torsion free groups which are virtual surface bundle groups of type I in Johnson's trichotomy may be realised by aspherical closed smooth 4-manifolds. (This was already known for type II.)

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 3 , December 2000 , pp. 353 - 356
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Eckmann, B. and Müller, H., ‘Poincaré duality groups of dimension two’, Comment. Math. Helv. 55 (1980), 510–520.CrossRefGoogle Scholar
[2]Johnson, F.E.A., ‘On the realizability of poly-surface groups’, J. Pure. Appl. Algebra 15 (1979), 235–241.CrossRefGoogle Scholar
[3]Johnson, F.E.A., ‘Extending group actions by finite groups. I’, Topology 31 (1992), 407–420.CrossRefGoogle Scholar
[4]Johnson, F.E.A., ‘A group theoretic analogue of the Parshin-Arakelov rigidity theorem’, Arch. Math. (Basel) 63 (1994), 354–361.CrossRefGoogle Scholar
[5]Johnson, F.E.A., ‘Finite coverings and surface fibrations’, J. Pure Appl. Algebra 112 (1996), 41–52.CrossRefGoogle Scholar
[6]Johnson, F.E.A., ‘A rigidity theorem for group extensions’, Archiv Math. (Basel) 73 (1999), 81–89.CrossRefGoogle Scholar
[7]Scott, G.P., ‘The geometries of 3-manifolds”, Bull. London Math. Soc. 15 (1983), 401–487.CrossRefGoogle Scholar