Automorphisms of graphs of groups with cyclic edge groups
Published in Submitted, 1900
We describe the outer automorphism group of a one-ended fundamental group of a graph of groups, when edge groups are cyclic, and vertex groups are torsion-free with cyclic centralisers. We show that in this case the outer automorphism group is virtually built from the outer automorphisms of the vertex groups (fixing some elements), the outer automorphisms of some associated generalised Baumslag-Solitar groups, and generalised twists - partial conjugations by elements in the centralisers of some elliptic elements in the group.