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

TL;DR

This paper introduces Chambord groups, a new family of groups constructed from braided strand diagrams, and proves that their polycyclic subgroups are virtually abelian and undistorted, advancing understanding of their geometric properties.

Contribution

The paper defines Chambord groups from semigroup presentations and establishes their key geometric properties, including subgroup structure and distortion characteristics.

Findings

Polycyclic subgroups are virtually abelian.

Polycyclic subgroups are undistorted.

Includes previously studied asymptotically rigid mapping class groups.

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.