Nonsmoothable, locally indicable group actions on the interval

Nonsmoothable Group Actions on Elliptic Surfaces

Let G be a cyclic group of order 3, 5 or 7, and X = E(n) be the relatively minimal elliptic surface with rational base. In this paper, we prove that under certain conditions on n, there exists a locally linear G-action on X which is nonsmoothable with respect to infinitely many smooth structures on X . This extends the main result of [18].

Amenable Groups with a Locally Invariant Order Are Locally Indicable

We show that every amenable group with a locally invariant partial order has a left-invariant total order (and is therefore locally indicable). We also show that if a group G admits a left-invariant total order, and H is a locally nilpotent subgroup of G, then a left-invariant total order on G can be chosen so that its restriction to H is both left-invariant and right-invariant. Both results fo...

On Morita Equivalence of Group Actions on Locally C-algebras

In this paper, we prove that two continuous inverse limit actions α and β of a locally compact group G on the locally C-algebras A and B are strongly Morita equivalent if and only if there is a locally C-algebra C such that A and B appear as two complementary full corners of C and there is a continuous action γ of G on C which leaves A and B invariant such that γ|A = α and γ|B = β. This general...

Universal Properties of Group Actions on Locally Compact Spaces

We study universal properties of locally compact G-spaces for countable infinite groups G. In particular we consider open invariant subsets of the G-space βG, and their minimal closed invariant subspaces. These are locally compact free G-spaces, and the latter are also minimal. We examine the properties of these G-spaces with emphasis on their universal properties. As an example of our results,...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras