Normalising graphs of groups
(16 pages)
Abstract.
We discuss a partial
normalisation of a finite graph of finite groups (\Gamma(-), X)
which leaves invariant the fundamental group. In conjunction with an
easy graph-theoretic result, this provides a flexible and rather
useful tool in the study of finitely generated virtually free
groups. Applications discussed here include (i) an important
inequality for the number of edges in a Stallings decomposition
\Gamma ~ \pi1(\Gamma(-), X) of a finitely generated virtually
free group, (ii) the proof of equivalence of a number of conditions
for such a group to be `large', as well as (iii) the classification up
to isomorphism of virtually free groups of (free) rank 2. We also
discuss some number-theoretic consequences of the last result.
The following versions are available:
Back to Christian Krattenthaler's
home page.