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Wed, 25 Jun 2025
15:00

Boundary cubulation is a pathway to residual finiteness

Thomas Ng
(Brandeis University)
Abstract

Actions on CAT(0) cube complexes are powerful geometric tool for both algebraically decomposing groups and establishing subgroup separability results.  I will describe boundaries associated to hyperbolic and relatively hyperbolic groups. With a focus on (quotients of) free products, I will discuss variations on a boundary criteria of Bergeron—Wise for exhibiting cocompact actions on CAT(0) cube complexes.  I will explain some ideas on how to use these tools to show that most (small-cancellation or random density) quotients of free products preserve residual finiteness. This is based on multiple joint works with subsets of Einstein, Krishna MS, Montee, and Steenbock.

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