相关论文: Configuration spaces and braid groups on graphs in…

We show that the homology over a field of the space of free maps from the n-sphere to the n-fold suspension of X depends only on the cohomology algebra of X and compute it explicitly. We compute also the homology of the closely related…

To a given tiling a non commutative space and the corresponding C*-algebra are constructed. This includes the definition of a topology on the groupoid induced by translations of the tiling. The algebra is also the algebra of observables for…

Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been…

A comprehensive theory for robust PID control in continuous-time and discrete-time domain is reviewed in this paper. For a given finite set of linear time invariant plants, algorithms for fast computation of robustly stabilizing regions in…

Consider a graph G with n vertices. In this paper we study geometric conditions for an n-tuple of points in R^d to admit a tensegrity with underlying graph G. We introduce and investigate a natural stratification, depending on G, of the…

We construct a class of Garside groupoid structures on the pure braid groups, one for each function (called labelling) from the punctures to the integers greater than 1. The object set of the groupoid is the set of ball decompositions of…

Micro-Aerial Vehicles (MAVs) have the advantage of moving freely in 3D space. However, creating compact and sparse map representations that can be efficiently used for planning for such robots is still an open problem. In this paper, we…

Planning for multi-robot teams in complex environments is a challenging problem, especially when these teams must coordinate to accomplish a common objective. In general, optimal solutions to these planning problems are computationally…

Various non-trivial spaces are becoming popular for embedding structured data such as graphs, texts, or images. Following spherical and hyperbolic spaces, more general product spaces have been proposed. However, searching for the best…

In this paper, we investigate the feasibility of using knowledge graphs to interpret actions and behaviors for robot manipulation control. Equipped with an uncalibrated visual servoing controller, we propose to use robot knowledge graphs to…

Autostackability for finitely generated groups is defined via a topological property of the associated Cayley graph which can be encoded in a finite state automaton. Autostackable groups have solvable word problem and an effective inductive…

We introduce the classical theory of the interplay between group theory and topology into the context of operads and explore some applications to homotopy theory. We first propose a notion of a group operad and then develop a theory of…

In this paper, we study graphical conditions for structural controllability and accessibility of drifted bilinear systems over Lie groups. We consider a bilinear control system with drift and controlled terms that evolves over the special…

We study two notions of being well-structured for classes of graphs that are inspired by classic model theory. A class of graphs $C$ is monadically stable if it is impossible to define arbitrarily long linear orders in vertex-colored graphs…

We construct classifying spaces for discrete and compact Lie groups, with the property that they are topological groups and complete metric spaces in a natural way. We sketch a program in view of extending these constructions.

We study the category whose objects are graphs of fixed genus and whose morphisms are contractions. We show that the corresponding contravariant module categories are Noetherian and we study two families of modules over these categories.…

This paper is a survey of the relationship between labelled configuration spaces, mapping class groups with marked points and function spaces. In particular, we collect calculations of the cohomology groups for the mapping class groups of…

We study the density of periodic configurations for shift spaces defined on (the Cayley graph of) a finitely generated group. We prove that in the case of a full shift on a residually finite group and in that of a group shift space on an…

Place classification is a fundamental ability that a robot should possess to carry out effective human-robot interactions. It is a nontrivial classification problem which has attracted many research. In recent years, there is a high…

In [9] we proved that the space of countable torsion-free abelian groups is Borel complete. In this paper we show that our construction from [9] satisfies several additional properties of interest. We deduce from this that countable…