A. Yaman

We show that given a Peano continuum $M$ if $M$ remains connected when any $n-3$ points are removed where $n\geq 4$ then a group of homeomorphism of $M$ cannot act properly discontinuously cocompactly on the space of distinct $n$-tuples of $M$.For this we understand the dynamics induced on $M$ from properly discontinuous action of the group on $\Theta_n(M)$, and prove that when $n\neq 3$ and $M$ satisfies the above properties these dynamics and cocompacity together give rise a contradiction.