In mathematics, the Thompson groups (also called Thompson's groups, vagabond groups or chameleon groups) are three groups, commonly denoted
F
⊆
T
⊆
V
{\displaystyle F\subseteq T\subseteq V}
, which were introduced by Richard Thompson in some unpublished handwritten notes in 1965 as a possible counterexample to the von Neumann conjecture. Of the three, F is the most widely studied, and is sometimes referred to as the Thompson group or Thompson's group.
The Thompson groups, and F in particular, have a collection of unusual...
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I want to learn about the structure of Thompson's group $V$, $F$ and $T$ and their properties. I also want to know about the properties of actions of these groups on $\mathbb{S}^1$ and the cantor set $\mathcal{C}$.
I am aware of the following books and references:
Office hours with a geometri...
Let $B:\mathcal{P}(X)\to\mathcal{P}(X)$ a function s.t.
$B(\emptyset)=\emptyset$
$B(A)=B(X - A)$
$B(B(A))\subset B(A)$
$A\cup B\cap B(A\cup B)=A\cup B\cap (B(A)\cup B(B))$
and $F:\mathcal{P}(X)\to\mathcal{P}(X)$ with $F(A)=A\cup B(A)$.
I want to show that $F$ is a closure function for the...
