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.
New examples show non-integer Hausdorff dimensions in collapsing spaces.
Classified spaces in low dimensions.
New property: polygons have a fixed dimension regardless of ambient space dimensions.
Short note shows unbounded dimensions in Fano K-moduli spaces.
The paper constructs Gromov-Hausdorff metrics for Lorentzian spaces and calculates dimensions.
Paper relates asymptotic dimension to cofinal dimension using coarse proximities.
We introduce a new quasi-isometry invariant of metric spaces called the hyperbolic dimension, hypdim, which is a version of the Gromov's asymptotic dimension, asdim. The hyperbolic dimension is at most the asymptotic dimension, however, unlike the asymptotic dimension, the hyperbolic dimension of any Euclidean space R^…
We construct a universal space for the class of proper metric spaces of bounded geometry and of given asymptotic dimension. As a consequence of this result, we establish coincidence of the asymptotic dimension with the asymptotic inductive dimensions.
Given a metric space of finite asymptotic dimension, we consider a quasi-isometric invariant of the space called dimension function. The space is said to have asymptotic Assouad-Nagata dimension less or equal if there is a linear dimension function in this dimension. We prove that if is a tree-graded space …
We consider the notion of dimension in four categories: the category of (unbounded) separable metric spaces and (metrically proper) Lipschitz maps, and the category of (unbounded) separable metric spaces and (metrically proper) uniform maps. A unified treatment is given to the large scale dimension and the small scale …
We discuss a variation of Gromov's notion of asymptotic dimension that was introduced and named Nagata dimension by Assouad. The Nagata dimension turns out to be a quasisymmetry invariant of metric spaces. The class of metric spaces with finite Nagata dimension includes in particular all doubling spaces, metric trees, …
We introduce a quasi-symmetry invariant of a metric space Z called the capacity dimension. Our main result says that for a visual Gromov hyperbolic space X the asymptotic dimension of X is at most the capacity dimension of its boundary at infinity plus 1.
In higher dimensions, Schottky spaces have unique topological properties.
Perimeter minimizers in curved spaces have a singular set no more than 5 dimensions.
New findings on metric spaces with finite Nagata dimension.
Researchers calculate cohomological dimensions of manifold configuration spaces, proving arithmeticity and providing bounds.
We study the Assouad dimension and the Nagata dimension of metric spaces. As a general result, we prove that the Nagata dimension of a metric space is always bounded from above by the Assouad dimension. Most of the paper is devoted to the study of when these metric dimensions of a metric space are locally given by the …
In the first part of the paper we show how to relate several dimension theories (asymptotic dimension with Higson property, asymptotic dimension of Gromov, and capacity dimension of Buyalo \cite{Buyalo1}) to Nagata-Assouad dimension. This is done by applying two functors on the Lipschitz category of metric spaces: micr…
New geometric flow equations describe how space-time dimensions change.
Corrects a 1-off error in Harer's spine dimension calculation for decorated Teichmüller spaces.
In this paper, we study the capacity dimension of the boundary of spaces. We first compare the two metrics on the boundary of a hyperbolic space, i.e., the visual metric and the conical metric, and prove that they give the same capacity dimension of the boundary. Then we study the capacity dimension o…
The study classifies stable submanifolds in product spaces of projective spaces.
Study stability of curvature-dimension condition for negative dimensions.
We study discrete groups from the view point of a dimension gap in connection to CAT(0) geometry. Developing studies by Brady-Crisp and Bridson, we show that there exist finitely presented groups of geometric dimension 2 which do not act properly on any proper CAT(0) spaces of dimension 2 by isometries, although such a…
Functional dimension varies in ReLU networks, with implications for symmetry and connectivity.
We obtain two in a sense dual to each other results: First, that the capacity dimension of every compact, locally self-similar metric space coincides with the topological dimension, and second, that the asymptotic dimension of a metric space, which is asymptotically similar to its compact subspace coincides with the to…
Study of self-dual polygons in higher dimensions, including explicit constructions and dimension calculations.
Proposes a new metric space example showing non-constant topological dimension.
Eluder dimension and information gain are equivalent for reproducing kernel Hilbert spaces.
We introduce the notion of large scale inductive dimension for asymptotic resemblance spaces. We prove that the large scale inductive dimension and the asymptotic dimensiongrad are equal in the class of r-convex metric spaces. This class contains the class of all geodesic metric spaces and all finitely generated groups…
New proof shows no negative curvature Einstein metrics in specific dimensions.
We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also enables us to expand the possible space where the dimension reduction functions bel…
Asymptotic dimension of planes and graphs is at most three.
We compute many dimensions of spaces of finite type invariants of virtual knots (of several kinds) and the dimensions of the corresponding spaces of "weight systems", finding everything to be in agreement with the conjecture that "every weight system integrates".
In this article we calculate the dimension of the Hilbert space of Kahler quantization of the moduli space of vortices on a Riemann surface. This dimension is given by the holomorphic Euler characteristic of the quantum line bundle.
Thurston's spine dimension exceeds virtual cohomological dimension.
Study shows infinite families of manifolds with nonnegative curvature.
A large class of vacuum space-times is constructed in dimension 4+1 from hyperboloidal initial data sets which are not small perturbations of empty space data. These space-times are future geodesically complete, smooth up to their future null infinity, and extend as vacuum space-times through their Cauchy horizon. Dime…
It is well-known that a paracompact space X is of covering dimension n if and only if any map f from X to a simplicial complex K can be pushed into its n-skeleton. We use the same idea to define dimension in the coarse category. It turns out the analog of maps f from X to K is related to asymptotically Lipschitz maps, …
Paper determines Assouad-Nagata dimension for all minor-closed metrics.
We study the mean dimension of the moduli space of Brody curves. We introduce the notion of "mean energy" and show that this can be used to estimate the mean dimension.
New theorem for nonlocal minimal surfaces in any dimension.
This paper classifies 13D manifolds based on Bazaikin spaces.
DSNE visualizes data velocity in lower dimensions.
This is a detailed introductory survey of the cohomological dimension theory of compact metric spaces.
We show that the algebraic dimension of a twistor space over n#CP^2 cannot be two if n>4 and the fundamental system (i.e. the linear system associated to the half-anti-canonical bundle, which is available on any twistor space) is a pencil. This means that if the algebraic dimension of a twistor space on n#CP^2, n>4, is…
The paper studies asymptotic dimensions of manifolds and spaces, proving key results about their geometric decompositions.
For an Alexandrov space (with curvature bounded below), we determine the maximal dimension of its isometry group and show that the space is isometric to a Riemannian manifold, provided the dimension of its isometry group is maximal. We also determine a gap in the possible dimensions of the isometry groups and show that…