# '22

36th Summer Topology Conference

July 18-22, 2022

University of Vienna, Department of Mathematics
Oskar-Morgenstern-Platz 1, 1090 Vienna, AUSTRIA

### "Residually finite quotients of free products"

#### Ng, Thomas

Small cancellation theory is a rich source of cocompactly cubulated groups. The classical $C’(1/6)$ condition has a natural generalization to quotients of free products. These quotients act on a Gromov hyperbolic polygonal complexes and have been used to exhibit infinite families of groups with exotic embedding properties. When the factor groups are assumed to act geometrically on a CAT$(0)$ cube complex, Martin and Steenbock show that such $C’(1/6)$ quotients are again cocompactly cubulated. I will describe joint work with Eduard Einstein (University of Pittsburgh) proving that when the free factors are residually finite any $C’(1/6)$ quotient is again residually finite. Our proof relies on showing that the quotient groups are relatively cubulated.

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