We classify the minimum volume smooth complex hyperbolic surfaces that admit smooth toroidal compactifications, and we explicitly construct their compactifications. There are five such surfaces and they are all arithmetic, i.e., they are associated with quotients of the ball by an arithmetic lattice. Moreover, the associated lattices are all commensurable. The first compactification, originally...

The degree to which engineering and social justice as fields of practice are (in)commensurable remains an open question. To illuminate important dimensions of that question, we explore intersections between those fields and two macro-sociological frameworks. Those theoretical frameworks—structural functionalism and social conflict—represent contrasting perspectives on how society should be orga...

In this paper we prove that if MK is the complement of a non-fibered twist knot K in S, then MK is not commensurable to a fibered knot complement in a Z/2Z-homology sphere. To prove this result we derive a recursive description of the character variety of twist knots and then prove that a commensurability criterion developed by D. Calegari and N. Dunfield is satisfied for these varieties. In ad...

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 classify the minimum volume smooth complex hyperbolic surfaces that admit smooth toroidal compactifications, and we explicitly construct their compactifications. There are five such surfaces and they are all arithmetic, i.e., they are associated with quotients of the ball by an arithmetic lattice. Moreover, the associated lattices are all commensurable. The first compactification, originally...

We find explicit models for the PSL2(C)and SL2(C)-character varieties of the fundamental groups of complements in S of an infinite family of two-bridge knots that contains the twist knots. We compute the genus of the components of these character varieties, and deduce upper bounds on the degree of the associated trace fields. We also show that these knot complements are fibered if and only if t...

Let β > 1 be a real number and M : R → GL(C) be a uniformly almost periodic matrix-valued function. We study the asymptotic behavior of the product Pn(x) = M(β x) · · ·M(βx)M(x). Under some condition we prove a theorem of Furstenberg-Kesten type for such products of non-stationary random matrices. Theorems of Kingman and Oseledec type are also proved. The obtained results are applied to multipl...

We discuss a specific way in which the notion of complementarity can be based on the dynamics of the system considered. This approach rests on an epistemic representation of system states, reflecting our knowledge about a system in terms of coarse grainings (partitions) of its phase space. Within such an epistemic quantization of classical systems, compatible, comparable, commensurable, and com...

Multi-criteria decision making (MCDM) is one of the most common activities in human society. It consists of selecting the optimal one from a set of available alternatives with respect to the predefined criteria or attributes. In this paper, a hybrid decision making approach integrating Analytical hierarchical process (AHP) operators into VIKOR is proposed for tackling multi criteria problems wi...