| Register
\(\newcommand{\Cat}{{\rm Cat}} \) \(\newcommand{\A}{\mathcal A} \) \(\newcommand{\freestar}{ \framebox[7pt]{$\star$} }\)

3. Dynamics and measurable combinatorics of group actions


    1. Add remark

      Problem 3.1.

      Let $d < n \in \omega$. Is there a compact subflow of the space of all bounded displacement actions of $\Z^d$ on $\Z^n$ with finitely many orbits?


        • Add remark

          Problem 3.2.

          Let $G$ be a Schreier graph of a free pmp (probability measure preserving) action of a finitely generated group $\Gamma$.
          1. If $\Gamma$ is non-amenable, does $G$ admit a measurable perfect matching?
          2. What if $\Gamma$ is just non-two ended and infinite?


            • Add remark

              Problem 3.3.

              Let $\Gamma$ be an infinite property (T) group. Let $G$ be one of the following:
              1. A Borel graphing of the orbit equivalence relation of a free pmp action of $\Gamma$.
              2. A Cayley graph of $\Gamma$.
              Does every finite graph appear as a minor of $G$?


                • Add remark

                  Problem 3.4.

                  Let $G$ be a Polish group and $N$ a locally compactable normal subgroup of $G$. Is the translation action of $N$ on $G$ hypersmooth? (It is if $N$ is countable.)

                      Cite this as: AimPL: Descriptive graph theory, available at http://aimpl.org/descriptgraph.