Related papers: Finding topology in a factory: configuration space…
The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…
This paper is intended to provide concrete examples of concepts discussed elsewhere in this volume, especially splittings of groups and non-positively curved cube complexes but also other things. The idea of the construction (configuration…
A classification of a family of 3-revolute (3R) positining manipulators is established. This classification is based on the topology of their workspace. The workspace is characterized in a half-cross section by the singular curves. The…
We present a mathematical framework for describing the topology of configuration spaces for particles on one-connected graphs. In particular, we compute the homology groups over integers for different classes of one-connected graphs. Our…
The topological complexity TC(X) is a homotopy invariant which reflects the complexity of the problem of constructing a motion planning algorithm in the space X, viewed as configuration space of a mechanical system. In this paper we…
On objects of a triangulated category with a stability condition, we construct a topology.
Understanding degrees of freedom in classical mechanics is fundamental to characterizing physical systems. Counting them is usually easy, especially if we can assign them a clear meaning. However, the precise definition of a degree of…
This work deals with the presence of topological structures in models of two real scalar fields in the two-dimensional spacetime. The subject concerns the presence of a geometric constriction, which appears with a modification of the…
In this article we introduce the space of configurations of commuting elements in a topological group and show that it satisfies rational homological stability for the sequences of unitary, special unitary and symplectic groups. We also…
We construct a real combinatorial model for the configuration spaces of points of compact smooth oriented manifolds without boundary. We use these models to show that the real homotopy type of configuration spaces of a simply connected such…
Understanding the geometry and topology of configuration or conformational spaces of molecules has relevant applications in chemistry and biology such as the proteins folding problem, drug design and the structure activity relationship…
We investigate the enumerative geometry of point configurations in projective space. We define "projective configuration counts": these enumerate configurations of points in projective space such that certain specified subsets are in fixed…
The discovery of correlated phases in twisted moir\'e superlattices accelerated the search for low-dimensional materials with exotic properties. A promising approach uses engineered substrates to strain the material. However, designing…
The structure of topological spaces is analysed here through the lenses of fibrous preorders. Each topological space has an associated fibrous preorder and those fibrous preorders which return a topological space are called spacial. A…
Understanding conformational change is crucial for programming and controlling the function of many mechanical systems such as allosteric enzymes and tunable metamaterials. Of particular interest is the relationship between the network…
This paper studies the configuration space of all possible positions of a linkage in R^n. For example, it shows that for every compact algebraic set, there is a linkage whose configuration space is analytically isomorphic to a finite number…
If $G$ is a graph with vertex set $V$, let Conf$_n^{\text{sink}}(G,V)$ be the space of $n$-tuples of points on $G$, which are only allowed to overlap on elements of $V$. We think of Conf$_n^{\text{sink}}(G,V)$ as a configuration space of…
We design a motion planning algorithm to coordinate the movements of two robots along a figure eight track, in such a way that no collisions occur. We use a topological approach to robot motion planning that relates instabilities in motion…
We study the geodesic complexity of the ordered and unordered configuration spaces of graphs in both the $\ell_1$ and $\ell_2$ metrics. We determine the geodesic complexity of the ordered two-point $\varepsilon$-configuration space of any…
On one hand, we study the class of graphs on surfaces, satisfying tessellation properties, with positive Forman curvature on each edge. Via medial graphs, we provide a new proof for the finiteness of the class, and give a complete…