缅北强奸

Title: Measure equivalence and wreath product groups

Abstract: Measure equivalence is an equivalence relation on the space聽of groups that was defined by Gromov in the 90's as an analytic聽analogue of quasi-isometry. Let F be a nonabelian free group. We show聽that if $L_1$ and $L_2$ are measure equivalent groups, then the wreath聽products $L_1\wr F$ and $L_2\wr F$ are measure equivalent with index.聽聽We also make several observations about the way one-ended groups can聽live inside a wreath product group $B\wr L$. In particular, we聽conclude that if $\phi$ is any automorphism of $B\wr L$ and $L$ is聽one-ended, then $\phi(L)$ is conjugate to $L$. This is joint work with聽Robin Tucker-Drob.