A right-angled Artin group (RAAG) is a group given by a finite presentation in which the only relations are that some of the generators commute. Free groups and free abelian groups are the extreme examples of RAAGs. Their automorphism groups GL(n, Z) and Out(F_n) are complicated and fascinating groups which have been extensively studied. In these lectures I will explain how to use what we know about GL(n, Z) and Out(F_n) to study the structure of the (outer) automorphism group of a general RAAG. This will involve both inductive local-to-global methods and the construction of contractible spaces on which these automorphism groups act properly. For the automorphism group of a general RAAG the space we construct is a hybrid of the classical symmetric space on which GL(n, Z) acts and Outer space with its action of Out(F_n).
展开▼
