Automorphism group actions in complex analysis

Tree actions of automorphism groups

We introduce conditions on a group action on a tree that are sufficient for the action to extend to the automorphism group. We apply this to two different classes of one-relator groups: certain BaumslagSolitar groups and one-relator groups with centre. In each case we derive results about the automorphism group, and deduce that there are relatively few outer automorphisms.

Math 311: Complex Analysis — Automorphism Groups Lecture

Aut(C) = {analytic bijections f : C −→ C}. Any automorphism of the plane must be conformal, for if f ′(z) = 0 for some z then f takes the value f(z) with multiplicity n > 1, and so by the Local Mapping Theorem it is n-to-1 near z, impossible since f is an automorphism. By a problem on the midterm, we know the form of such automorphisms: they are f(z) = az + b, a, b ∈ C, a 6= 0. This description...

The Automorphism Group of a Homogeneous Almost Complex Manifold (*)

The Automorphism Group of the Complex of Pants Decompositions

There has been recent interest in finding combinatorial models for groups, i.e. finding a simplicial complex whose automorphism group is a given group. For example, CharneyDavis showed that the Coxeter Diagram is a model for Out(W ) (for certain Coxeter groups W) [3], and Bridson-Vogtmann showed that a spine of Outer Space is a model for Out(Fn) [1]. In this paper, we prove that the complex of ...

AUTOMORPHISM GROUP OF GROUPS OF ORDER pqr

H"{o}lder in 1893 characterized all groups of order $pqr$ where  $p>q>r$ are prime numbers. In this paper,  by using new presentations of these groups, we compute their full automorphism group.