The isometry group of outer space
Royden's Theorem for Teichmüller space says that in sufficiently high genus, the isometry group of Teichmüller space with the Teichmüller metric is the extended mapping class group. The authors establish an analogue of this theorem for Culler--Vogtmann Outer Space \(CV_n\), showing that for \(n\) sufficiently large, its isometry group with the Lipschitz metric is \(\text{Out}(F_n)\). As is typical in the theory, a result analogous to one in Teichmüller theory is proven by completely different methods. The methods used in the present article concern the local structure and non--homogeneity of \(CV_n\).
scientific article; zbMATH DE number 6094103
scientific article