Related papers: Asymptotic resemblance relations on groups

We study the relations between the projective and the almost conformally symplectic structures on a smooth even dimensional manifold. We describe these relations by a single almost conformally symplectic connection with totally trace--free…

We give a method of constructing maps between tubular groups inductively according to a set of strategies. This map will be a quasi-isometry exactly when the set of strategies is consistent. Conversely, if there exists a quasi-isometry…

In this paper we develop the theory of Artin-Wraith glueings for topological spaces. As an application, we show that some categories of compactifications of coarse spaces that agree with the coarse structures are invariant under coarse…

This is my dissertation. Its research object is a symmetric group of permutations acting on a finite set. The density of permutations with a given cycle structure pattern is explored when the group order tends to infinity. New and sharper…

Commensurate scale relations are perturbative QCD predictions which relate observable to observable at fixed relative scale, such as the "generalized Crewther relation", which connects the Bjorken and Gross-Llewellyn Smith deep inelastic…

In this paper, we study asymptotic behavior arising in inverse limit spaces of dendrites. In particular, the inverse limit is constructed with a single unimodal bonding map, for which points have unique itineraries and the critical point is…

The asymptotic structure of AdS spacetimes in the context of General Relativity coupled to the Maxwell field in three spacetime dimensions is analyzed. Although the fall-off of the fields is relaxed with respect to that of Brown and…

We give various characterizations of the covering dimension of the limit space of a contracting self-similar group. In particular, we show that it is equal to the minimal dimension of a contracting affine model, to the asymptotic dimension…

In the In recent times, the research community has explored diverse structures and novel fabrication methods for amorphous solids. This work investigates structural trends among different classes of amorphous materials to identify universal…

A quandle is an algebraic structure which attempts to generalize group conjugation. These structures have been studied extensively due to their connections with knot theory, algebraic combinatorics, and other fields. In this work, we…

We prove the dynamic asymptotic dimension of a free isometric action on a space of finite doubling dimension is either infinite or equal to the asymptotic dimension of the acting group; and give a full description of the dynamic asymptotic…

We extend the comatrix coring to the case of a quasi-finite bicomodule. We also generalize some of its interesting properties. We study equivalences between categories of comodules over rather general corings. We particularize to the case…

We compute the asymptotic dimension of the rationals given with an invariant proper metric. Also, we show that a countable torsion abelian group taken with an invariant proper metric has asymptotic dimension zero.

The survey covers several topics related to the asymptotic structure of various combinatorial and analytic objects such as the path spaces in graded graphs (Bratteli diagrams), invariant measures with respect to countable groups, etc. The…

Symmetry is at the heart of much of mathematics, physics, and art. Traditional geometric symmetry groups are defined in terms of isometries of the ambient space of a shape or pattern. If we slightly generalize this notion to allow the…

For any dynamical system $T:X\rightarrow X$ of a compact metric space $X$ with $g-$almost product property and uniform separation property, under the assumptions that the periodic points are dense in $X$ and the periodic measures are dense…

It is proved that the assembly maps in algebraic K- and L-theory with respect to the family of finite subgroups is injective for groups with finite asymptotic dimension that admit a finite model for the classifying space for proper actions.…

In the framework of the connection theory, a contravariant analog of the Sternberg coupling procedure is developed for studying a natural class of Poisson structures on fiber bundles, called coupling tensors. We show that every Poisson…

Lipschitz equivalence of self-similar sets is an important area in the study of fractal geometry. It is known that two dust-like self-similar sets with the same contraction ratios are always Lipschitz equivalent. However, when self-similar…

In this paper, we determine the asymptotic dimension for all surface braid groups -- including those associated with non-orientable and infinite-type surfaces -- as well as for torsion-free poly-finitely generated surface groups. We…