Asymptotically rigid mapping class groups II: strand diagrams and nonpositive curvature

Abstract

In this article, we introduce a new family of groups, called Chambord groups and constructed from braided strand diagrams associated to specific semigroup presentations. It includes the asymptotically rigid mapping class groups previously studied by the authors such as the braided Higman-Thompson groups and the braided Houghton groups. Our main result shows that polycyclic subgroups in Chambord groups are virtually abelian and undistorted.

47 pages, 23 figures. Minor revisions. Accepted for publication in Transactions of the AMS