The classical symmetric space $Q_n$ of positive definite quadratic forms and Culler Vogtmann Outer Space CV$_n$ are major tools in the study of GL($n, Z$) and Out($F_n$), respectively. The class of right-angled Artin groups (RAAGs) is a natural extension of free groups and free abelian groups, which has featured prominently in the study of CAT(0) cube complexes and low-dimensional topology. Let $A$ be a RAAG. We build a finite-dimensional, contractible outer space $O_A$ on which Out($A$) acts with finite point stabilizers. This construction generalizes that of $Q_n$ and CV$_n$ and blends features of both. In this talk, we will describe the construction of $O_A$, then discuss open questions and directions for further study. This is joint work with Ruth Charney and Karen Vogtmann.
By Yair Minsky
By Ursula Hamenstädt
By Dawid Kielak
By Radhika Gupta
By Anne Lonjou
By Piotr Przytycki
By Vincent Guirardel
By Federica Fanoni
By Corey Bregman
By Richard D. Wade
By Sebastian Hensel
By Olga Mula Hernandez
By François-Xavier Vialard
By Elsa Cazelles
By Thibaut Le Gouic
By Jérôme Dedecker
By François-Xavier Vialard
By Thibaut Le Gouic
By Jean Feydy
By Elsa Cazelles
By Olga Mula Hernandez
