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THE NIELSEN METHOD FOR GROUPS ACTING ON TREES

Published online by Cambridge University Press:  09 July 2002

RICHARD WEIDMANN
RICHARD WEIDMANN
Affiliation:
Fakultät für Mathematik, Ruhr-Universität Bochum, D-44780 Bochum, Germany. [email protected]
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Abstract

We use Nielsen methods to study generating sets of subgroups of groups that act on simplicial trees and give several applications. In particular, we exhibit an explicit bound for the complexity of acylindrical splittings of a finitely generated group in terms of its rank. This is applied to JSJ-splittings of word-hyperbolic groups and 3-manifolds. As a last application we construct examples of amalgamated products that show that there exists no non-trivial rank formula for amalgamated products.

2000 Mathematical Subject Classification: 20E06, 20E08, 57M27.

Keywords

Nielsen method Bass-Serre theory acylindricity
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 85 , Issue 1 , March 2002 , pp. 93 - 118
Copyright
2002 London Mathematical Society

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