相关论文: Configuration spaces and braid groups on graphs in…
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…
This is a glossary of notions and methods related with the topological theory of collections of affine planes, including braid groups, configuration spaces, order complexes, stratified Morse theory, simplicial resolutions, complexes of…
In manipulation tasks, a robot interacts with movable object(s). The configuration space in manipulation planning is thus the Cartesian product of the configuration space of the robot with those of the movable objects. It is the complex…
Dimer coverings (or perfect matchings) of a finite graph are classical objects of graph theory appearing in the study of exactly solvable models of statistical mechanics. We introduce more general dimer labelings which form a topological…
Finitely many hypersurfaces are removed from unordered configuration spaces of $n$ points in $\mathbb{C}$ to obtain a fibration over unordered configuration spaces of $n-1$ complex points. Fundamental groups of these restricted…
We consider the braid groups $\mathbf{B}_n(X)$ on finite simplicial complexes $X$, which are generalizations of those on both manifolds and graphs that have been studied already by many authors. We figure out the relationships between…
We give explicit formulas for the asymptotic Betti numbers, over an arbitrary field, of the ordered configuration spaces of a graph. In characteristic zero, we further give explicit formulas for the asymptotic multiplicities in homology of…
We introduce the notion of graphical discreteness to group theory. A finitely generated group is graphically discrete if whenever it acts geometrically on a locally finite graph, the automorphism group of the graph is compact-by-discrete.…
We investigate the configuration space $\mathcal{S}_{G,b,\ell}$ associated with the movement of a robotic arm of length $\ell$ on a grid over an underlying graph $G$, anchored at a vertex $b \in G$. We study an associated PIP (poset with…
Systematic enumeration and identification of unique 3D spatial topologies of complex engineering systems (such as automotive cooling systems, electric power trains, satellites, and aero-engines) are essential to navigation of these…
Autonomous robotic inspection, where a robot moves through its environment and inspects points of interest, has applications in industrial settings, structural health monitoring, and medicine. Planning the paths for a robot to safely and…
The automorphisms of free groups with boundaries form a family of groups A_{n,k} closely related to mapping class groups, with the standard automorphisms of free groups as A_{n,0} and (essentially) the symmetric automorphisms of free groups…
In this paper we study the spaces of $q$-tuples of points in a Euclidean space, without $k$-wise coincidences (configuration-like spaces). A transitive group action by permuting these points is considered, and some new upper bounds on the…
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…
Soft robots, inspired by elephant trunks or octopus arms, offer extraordinary flexibility to bend, twist, and elongate in ways that rigid robots cannot. However, their motion planning remains a challenge, especially in cluttered…
We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of…
Path planning for multiple robots is well studied in the AI and robotics communities. For a given discretized environment, robots need to find collision-free paths to a set of specified goal locations. Robots can be fully anonymous,…
Configuration spaces of many real mechanical systems appear to be manifolds with singularity. A singularity often indicates that geometry of motion may change at the singular point of configuration space. We face conceptual problem…
We exhibit an algorithm with continuous instructions for two robots moving without collisions on a track shaped as a wedge of three circles. We show that the topological complexity of the configuration space associated with this problem is…
We provide a novel family of generative block-models for random graphs that naturally incorporates degree distributions: the block-constrained configuration model. Block-constrained configuration models build on the generalised…