相关论文: Configuration spaces and braid groups on graphs in…
Braiding defects in topological stabiliser codes has been widely studied as a promising approach to fault-tolerant quantum computing. We present a no-go theorem that places very strong limitations on the potential of such schemes for…
This is a draft of a book submitted for publication by the AMS. Its theme is the remarkable interplay, accelerating in the last few decades, between topology and the theory of orderable groups, with applications in both directions. It…
This paper studies the configuration spaces of linkages whose underlying graph is a single cycle. Assume that the edge lengths are such that there are no configurations in which all the edges lie along a line. The main results are that,…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…
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…
The aim of this article is to provide space level maps between configuration spaces of graphs that are predicted by algebraic manipulations of cellular chains. More explicitly, we consider edge contraction and half-edge deletion, and…
Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings…
All rational homology groups of unordered configuration spaces of the Moebius strip and the projective plane are calculated
We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complete graph with vertices as the points of $A \subseteq…
We discuss groups corresponding to Kohno Lie algebra of infinitesimal braids and actions of such groups. We construct homomorphisms of Lie braid groups to the group of symplectomorphisms of the space of point configurations in $R^3$ and to…
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…
Controlling a team of robots in a coordinated manner is challenging because centralized approaches (where all computation is performed on a central machine) scale poorly, and globally referenced external localization systems may not always…
In this paper we study the embedded topology of reducible plane curves having a smooth irreducible component. In previous studies, the relation between the topology and certain torsion classes in the Picard group of degree zero of the…
We introduce a computational framework for the topology optimization of cellular structures with spatially varying architecture, which is applied to functionally graded truss lattices under quasistatic loading. We make use of a first-order…
We characterise rigid graphs for cylindrical normed spaces $Z=X\oplus_\infty \mathbb{R}$ where $X$ is a finite dimensional real normed linear space and $Z$ is endowed with the product norm. In particular, we obtain purely combinatorial…
The program of understanding Shape Theory layer by layer topologically and geometrically -- proposed in Part I -- is now addressed for 4 points in 1-$d$. Topological shape space graphs are far more complex here, whereas metric shape spaces…
Assembly of large scale structural systems in space is understood as critical to serving applications that cannot be deployed from a single launch. Recent literature proposes the use of discrete modular structures for in-space assembly and…
We determine the topological complexity of unordered configuration spaces on almost all punctured surfaces (both orientable and non-orientable). We also give improved bounds for the topological complexity of unordered configuration spaces…
Formation control deals with the design of decentralized control laws that stabilize agents at prescribed distances from each other. We call any configuration that satisfies the inter-agent distance conditions a target configuration. It is…