A holomorphic quadratic differential on a hyperbolic Riemann surface has an associated measured foliation, which can be straightened to yield a measured geodesic lamination. On the other hand, a quadratic differential can be considered as the Schwarzian derivative of a CP1 structure, to which one can naturally associate another measured geodesic lamination (using grafting). We compare these two...

in this paper, we presented algebroids and crossed modules of algebroids. we also presented pullback crossed module of algebroids and we then define pushout crossed modules of algebroids.

In the definition of a crossed module $(T,G,rho)$, the actions of the group $T$ and $G$ on themselves are given by conjugation. In this paper, we consider these actions to be arbitrary and thus generalize the concept of ordinary crossed module. Therefore, we get the category ${bf GCM}$, of all generalized crossed modules and generalized crossed module morphisms between them, and investigate som...

Crossed Uncrossed Differentials (CUDs) have long been used as surrogate for the interhemispheric transfer time (IHTT). Evidence is presented that macular vision is the province of the major hemisphere, wherein all commands are initiated regardless of the laterality of the effectors of such commands. Using clinical and time-resolved data it is shown also that the above arrangement (i.e. neural h...

In this article, the notions of non-abelian tensor and exterior products of two normal crossed submodules of a given crossed module of groups are introduced and some of their basic properties are established. In particular, we investigate some common properties between normal crossed modules and their tensor products, and present some bounds on the nilpotency class and solvability length of the...

–a notion of amenability for topological semigroups is introduced. a topological semigroup s iscalled johnson amenable if for every banach s -bimodule e , every bounded crossed homomorphism froms to e* is principal. in this paper it is shown that a discrete semigroup s is johnson amenable if and only if1(s) is an amenable banach algebra. also, we show that if a topological semigroup s is johns...

A. M. S. Classification: 18G30, 18G55.