We give a necessary and sufficient condition for a locally compact group to be isomorphic to a closed cocompact subgroup in the isometry group of a Diestel–Leader graph. As a consequence of this condition, we see that every cocompact lattice in the isometry group of a Diestel–Leader graph admits a transitive, proper action on some other Diestel–Leader graph. We also give some examples of lattic...

We prove geometric superrigidity for actions of cocompact lattices in semisimple Lie groups of higher rank on infinite dimensional Riemannian manifolds of nonpositive curvature and finite telescopic dimension.

Tau is one of several types of microtubule-associated proteins (MAPs), responsible for the assembly and stability of microtubule networks that is present only in neurons and predominantly localized in axons which its functions are tightly regulated by phosphorylation. Via as yet unknown mechanisms, tau becomes hyperphosphorylated and accompanies with neuronal degeneration, loss of synapses...

A topoframe, denoted by $L_{ tau}$, is a pair $(L, tau)$ consisting of a frame $L$ and a subframe $ tau $ all of whose elements are complementary elements in$L$. $f$-ring $mathcal{R}(L_{ tau})$ is equal to the set $${fin Frm(mathcal{P}(mathbb R), L): f(mathfrak{O}(mathbb R))subseteq tau} .$$ In this paper, for every complemented element $ain L$ with $a, a'...

In this paper, we introduce the notions of expansion of ideals in $MV$-algebras, $ (tau,sigma)- $primary, $ (tau,sigma)$-obstinate  and $ (tau,sigma)$-Boolean  in $ MV- $algebras. We investigate the relations of them. For example, we show that every $ (tau,sigma)$-obstinate ideal of an $ MV-$ algebra is $ (tau,sigma)$-primary  and $ (tau,sigma)$-Boolean. In particular, we define an expansion $ ...

We show that any finitely generated group quasi-isometric to complex hyperbolic space is a finite extension of a properly discontinuous, cocompact subgroup of the isometry group.

This paper is about geometric and topological properties of a proper CAT(0) spaceX which is cocompact i.e. which has a compact generating domain with respect to the full isometry group. It is shown that geodesic segments in X can “almost” be extended to geodesic rays. A basic ingredient of the proof of this geometric statement is the topological theorem that there is a top dimension d in which ...