A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Computes fundamental groups of restricted configuration spaces.
Study shows configuration spaces' homological dimension increases monotonically.
We study the configuration space of equilateral and equiangular spatial hexagons for any bond angle by giving explicit expressions of all the possible shapes. We show that the chair configuration is isolated, whereas the boat configuration allows one-dimensional deformations which form a circle in the configuration spa…
Quantum groups created from disk configuration space homologies.
Researchers create a model for surface point configurations.
Study orders of canonical bundles over graph configuration spaces.
The square-peg problem is solved using configuration spaces and multijet transversality.
This expository article describes applications of topological configuration spaces to the control of robotic systems. In particular, we review recent work by the authors on configuration spaces of graphs. These are lovely spaces: we show for example that the configuration space of two points on the complete graph of fi…
Sharp upper bound for quasi polynomial degree of manifold configuration spaces.
This paper extends homological stability results for configuration spaces of manifolds.
We compute the fundamental group of various spaces of Desargues configurations in complex projective spaces: planar and non-planar configurations, with a fixed center and also with an arbitrary center.
Study on disk configurations in strips shows stability patterns.
Classifies graph configuration spaces homeomorphic to manifolds.
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 articulated graphs and banana graphs. We also complete the computation in the case of tre…
We prove homological stability for sequences of "oriented configuration spaces" as the number of points in the configuration goes to infinity. These are spaces of configurations of n points in a connected manifold M of dimension at least 2 which 'admits a boundary', with labels in a path-connected space X, and with an …
Decouples homotopy quotients of generalised configuration spaces on surfaces.
Researchers calculate cohomological dimensions of manifold configuration spaces, proving arithmeticity and providing bounds.
Research connects Lie algebras to configuration space (co)homology.
We compute the Betti numbers and describe the cohomology algebras of the ordered and unordered configuration spaces of three points in complex projective spaces, including the infinite dimensional case. We also compute these invariants for the configuration spaces of three collinear and non-collinear points.
The study examines when a section exists for graph configuration spaces.
Solves Plateau-Douglas problem for singular configurations in general metric spaces.
Using results on the topology of moduli space of polygons [Jaggi, 92; Kapovich and Millson, 94], it can be shown that for a planar robot arm with segments there are some values of the base-length, , at which the configuration space of the constrained arm (arm with its end effector fixed) has two disconnected com…
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 of copies of the algebraic set. If flexible edges are allowed, any compact set …
We show that the configuration space over a manifold M inherits many curvature properties of the manifold. For instance, we show that a lower Ricci curvature bound on M implies for the configuration space a lower Ricci curvature bound in the sense of Lott-Sturm-Villani, the Bochner inequality, gradient estimates and Wa…
Proves conjecture on graph configuration spaces' complexity.
Paper addresses hidden faces in configuration space integrals for embeddings.
We determine explicit formulas for geodesics (in the Euclidean metric) in the configuration space of ordered pairs (x,x') of points in R^n which satisfy d(x,x')>=epsilon. We interpret this as two or three (depending on the parity of n) geodesic motion-planning rules for this configuration space. In the associated unord…
We prove a transversality "lifting property" for compactified configuration spaces as an application of the multijet transversality theorem: the submanifold of configurations of points on an arbitrary submanifold of Euclidean space may be made transverse to any submanifold of the configuration space of points in Euclid…
Algorithm calculates stable multiplicities in cohomology of configuration spaces.
The paper improves bounds on how many squares can fit in a rectangle and still have stable homology.
We study configuration space integral formulas for Milnor's homotopy link invariants, showing that they are in correspondence with certain linear combinations of trivalent trees. Our proof is essentially a combinatorial analysis of a certain space of trivalent "homotopy link diagrams" which corresponds to all finite ty…
Summary of pure cactus groups and circle points.
Study on the topology of ordered disc configurations, revealing nontrivial homotopy classes.
A pair of points in a riemannian manifold makes a secure configuration if the totality of geodesics connecting them can be blocked by a finite set. The manifold is secure if every configuration is secure. We investigate the security of compact, locally symmetric spaces.
We generalize Fulton and MacPherson's configuration space construction to weighted filtered manifolds.
All rational homology groups of unordered configuration spaces of the Moebius strip and the projective plane are calculated
The space of marked n distinct points on the complex projective line up to projective transformations will be called a configuration space in this paper. There are two families of complex hyperbolic structures on the configuration space constructed by Deligne-Mostow and Thurston. We first confirm that these families ar…
A new overlapping space solves the configuration search problem for graph embeddings.
We construct a spectral sequence converging to the Morava -theory of unordered configuration spaces and identify its E-page as the homology of a Chevalley-Eilenberg-like complex for Hecke Lie algebras. Based on this, we compute the -theory of the weight summands of iterated loop spaces of spheres (paramet…
A 2-manifold's group structure is deduced from orbit configuration spaces.
Study of circle configurations in the plane, proving aspherical space and computing fundamental groups.
The paper classifies holomorphic maps between Riemann surface configuration spaces.
For Gamma a finite, connected metric graph, we consider the space of configurations of n points in Gamma with a restraint parameter r dictating the minimum distance allowed between each pair of points. These restricted configuration spaces come up naturally in topological robotics. In this paper, we study the homotopy,…
We use the compression theorem (arxiv:math.GT/9712235) cf section 7, to prove results for equivariant configuration spaces analogous to the well-known non-equivariant results of May, Milgram and Segal.
Study spider mechanism configuration spaces using squared distance function.
Non-trivial action on surface configuration homology.
We use rational formality of configuration spaces and the bar construction to study the cohomology of the space of braids in dimension four or greater. We provide a diagram complex for braids and a quasi-isomorphism to the de Rham cochains on the space of braids. The quasi-isomorphism is given by a configuration space …
The configuration space of the reduced Hamiltonian formulation of quantum gravity has been shown, for non-Ricci flat metrics, to be a higher-dimensional analogue of the Teichmüller space of conformal structures on a Riemann surface. In this article we show that the configuration space of conformal connection-dynamics i…