Cost of inner amenable groupoids

Structural Properties of Inner Amenable Discrete Groups

Extensions of amenable groups by recurrent groupoids

We show that amenability of a group acting by homeomorphisms can be deduced from a certain local property of the action and recurrency of the orbital Schreier graphs. This applies to a wide class of groups, amenability of which was an open problem, as well as unifies many known examples to one general proof. In particular, this includes Grigorchuk’s group, Basilica group, groups associated with...

structural properties of inner amenable discrete groups

Invariant Means and the Structure of Inner Amenable Groups

We study actions of countable discrete groups which are amenable in the sense that there exists a mean on X which is invariant under the action of G. Assuming that G is nonamenable, we obtain structural results for the stabilizer subgroups of amenable actions which allow us to relate the first `-Betti number of G with that of the stabilizer subgroups. An analogous relationship is also shown to ...

Actions of vector groupoids

In this work we deal with actions of vector groupoid which is a new concept in the literature‎. ‎After we give the definition of the action of a vector groupoid on a vector space‎, ‎we obtain some results related to actions of vector groupoids‎. ‎We also apply some characterizations of the category and groupoid theory to vector groupoids‎. ‎As the second part of the work‎, ‎we define the notion...