Related papers: Finding topology in a factory: configuration space…
We compute small rational models for configuration spaces of points on oriented surfaces, as right modules over the framed little disks operad. We do this by splitting these surfaces in unions of several handles. We first describe rational…
In this paper we present an implementation of a computer algorithm that automatically determines the topological structure of spacetime, using a branched covering space representation. This algorithm is applied to a few simple examples in…
It has been observed that the very important motion planning problem of robotics mathematically speaking boils down to the problem of finding a section to the path-space fibration, raising the notion of topological complexity, as introduced…
We show how to use topological ideas, such as compactness, to establish orderability properties of infinite groups. A new application is to provide a left-ordering for the group of PL homeomorphisms of a connected surface with boundary…
Finite automata were used to determine multiple addresses in number systems and to find topological properties of self-affine tiles and finite type fractals. We join these two lines of research by axiomatically defining automata which…
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…
Let $X$ be the space of isometry classes of ordered sextuples of points in the hyperbolic plane such that the product of the six corresponding rotations of angle $\pi$ is the identity. This space $X$ is closely related to the…
In this paper we determine the topological complexity of configuration spaces of graphs which are not necessarily trees, which is a crucial assumption in previous results. We do this for two very different classes of graphs: fully…
One of the primary methods of studying the topology of configurations of points in a graph and configurations of disks in a planar region has been to examine discrete combinatorial models arising from the underlying spaces. Despite the…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…
Wheeler emphasized the study of Superspace - the space of 3-geometries on a spatial manifold of fixed topology. This is a configuration space for GR; knowledge of configuration spaces is useful as regards dynamics and QM.In this Article I…
Grasping mechanisms must both create and subsequently hold grasps that permit safe and effective object manipulation. Existing mechanisms address the different functional requirements of grasp creation and grasp holding using a single…
We introduce the topological complexity of the work map associated to a robot system. In broad terms, this measures the complexity of any algorithm controlling, not just the motion of the configuration space of the given system, but the…
We discuss the principle tools and results and state a few open problems concerning the classification and topology of plane sextics and trigonal curves in ruled surfaces.
This paper focuses on studying the configuration spaces of graphs realised in $\mathbb C^2$, such that the configuration space is, after normalisation, one dimensional. If this is the case, then the configuration space is, generically, a…
This expository paper explores the interaction of group ordering with topological questions, especially in dimensions 2 and 3. Among the topics considered are surfaces, braid groups, 3-manifolds and their structures such as foliations and…
This is a brief introduction to the basic concepts of topology. It includes the basic constructions, discusses separation properties, metric and pseudometric spaces, and gives some applications arising from the use of topology in computing.
Certain geometric properties of submanifolds of configuration space are numerically investigated for classical lattice phi^4 models in one and two dimensions. Peculiar behaviors of the computed geometric quantities are found only in the…