# '22

36th Summer Topology Conference

July 18-22, 2022

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

### "Subgroups of $PL_+ I$ which do not embed into Thompson's group $F$"

#### Moore, Justin

We give a general criterion --- the existence of an $F$-obstruction --- for showing that a subgroup of $PL_+ I$ does not embed into Thompson's group $F$. An immediate consequence is that Cleary's golden ratio group $F_\tau$ does not embed into $F$, answering a question of Burillo, Nucinkis, and Reves. Our results also yield a new proof that Stein's groups $F_{p,q}$ do not embed into $F$, a result first established by Lodha using his theory of coherent actions. This is joint work with James Hyde.

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