arXiv research

Proves universal pairing result for 2-complexes, showing lack of positivity.

Constructs a universal Cannon-Thurston map for a new curve complex.

Study of universal complexes in toric topology with applications in category theory.

This research finds three meta-indicators for university rankings.

Complex-valued neural networks can approximate any continuous function.

We determine the algebraic structure underlying the geometric complex associated to a link in Bar-Natan's geometric formalism of Khovanov's link homology theory (n=2). We find an isomorphism of complexes which reduces the complex to one in a simpler category. This reduction enables us to specify exactly the amount of i…

We explore the complex associated to a link in the geometric formalism of Khovanov's (n=2) link homology theory, determine its exact underlying algebraic structure and find its precise universality properties for link homology functors. We present new methods of extracting all known link homology theories directly from…

Characterizes compact complex surfaces with finite homotopy rank-sum.

The Euler characteristic is the only additive topological invariant for spaces of certain sort, in particular, for manifolds with some finiteness properties. A generalization of the notion of a manifold is the notion of a V-manifold. Here we discuss a universal additive topological invariant of V-manifolds: the univers…

We study the geometry of universal embedding spaces for compact almost complex manifolds of a given dimension. These spaces are complex algebraic analogues of twistor spaces that were introduced by J-P. Demailly and H. Gaussier. Their original goal was the study of a conjecture made by F. Bogomolov, asserting the "tran…

We formalize an equivariant version of Bestvina-Brady discrete Morse theory, and apply it to Vietoris-Rips complexes in order to exhibit finite universal spaces for proper actions for all asymptotically CAT(0) groups.

Study properties of balanced hyperbolic compact complex manifolds.

Croke and Kleiner constructed two homeomorphic locally CAT(0) complexes whose universal covers have visual boundaries that are not homeomorphic. We construct two homeomorphic locally CAT(0) complexes so that the visual boundary of one universal cover contains a nonplanar graph, while the visual boundary of the other do…

We give a new and simple proof for the computation of the oriented and the unoriented fold cobordism groups of Morse functions on surfaces. We also compute similar cobordism groups of Morse functions based on simple stable maps of 3-manifolds into the plane. Furthermore, we show that certain cohomology classes associat…

The paper presents a chain complex for 3-manifold covers, including surface bundles and surgeries.

Physics: Similar long-distance properties can mask vastly different short-distance metrics.

We construct geometrically a homeomorphism between the moduli space of polynomial quadratic differentials on the complex plane and light-like polygons in the 2-dimensional Einstein Universe. As an application, we find a class of minimal Lagrangian maps between ideal polygons in the hyperbolic plane.

Counterexample found for Stein property of certain solvable Lie groups.

Complex-valued neural networks can approximate any continuous function with bounded widths and depths.

Sumformer simplifies Transformers to handle long sequences efficiently.

We show that the canonical contact structure on the link of a normal complex singularity is universally tight. As a corollary we show the existence of closed, oriented, atoroidal 3-manifolds with infinite fundamental groups which carry universally tight contact structures that are not deformations of taut (or Reebless)…

In the first part of the paper we describe the complex geometry of the universal Teichmüller space $\mathcal T$, which may be realized as an open subset in the complex Banach space of holomorphic quadratic differentials in the unit disc. The quotient $\mathcal S$ of the diffeomorphism group of the circle modulo Möbius …

Given an $L^2$-acyclic connected finite $CW$-complex, we define its universal $L^2$-torsion in terms of the chain complex of its universal covering. It takes values in the weak Whitehead group $\operatorname{Wh}^w(G)$. We study its main properties such as homotopy invariance, sum formula, product formula and Poincaré d…

This research formalizes uncertainty quantification for Universal Differential Equations models.

In genus two and higher, the fundamental group of a closed surface acts naturally on the curve complex of the surface with one puncture. Combining ideas from previous work of Kent--Leininger--Schleimer and Mitra, we construct a universal Cannon--Thurston map from a subset of the circle at infinity for the closed surfac…

Researchers prove no unexpected relations between complex manifold numbers.

Paper explores universal rates of ERM in machine learning.

Study of Hitchin moduli spaces over Teichmüller space.

Softmax attention approximates complex functions and subsumes many known universal approximators.

Abstract: Study of metrics on line bundles over complex varieties.

The paper discusses $q$-deformations of the Aomoto complex.

The problem of universal outlying sequence detection is studied, where the goal is to detect outlying sequences among $M$ sequences of samples. A sequence is considered as outlying if the observations therein are generated by a distribution different from those generating the observations in the majority of the sequenc…

Complex group cohomology surprisingly simple.

Framework for universal graph function approximators outperforms existing methods.

We prove that the universal Teichmuller space T(1) carries a new structure of a complex Hilbert manifold. We show that the connected component of the identity of T(1), the Hilbert submanifold T_{0}(1), is a topological group. We define a Weil-Petersson metric on T(1) by Hilbert space inner products on tangent spaces, c…

The main theorem is that if K is a finite CW complex with finite fundamental group G and universal cover homotopy equivalent to a product of spheres X, then G acts smoothly and freely on X x S^n for any n greater than or equal to the dimension of X. If the G-action on the universal cover of K is homologically trivial t…

Determines algebra structure of complex differential forms operators.

Automorphisms of contact graphs match those of ${ m CAT(0)}$ cube complexes under weak conditions.

We prove a very general Kobayashi-Hitchin correspondence on arbitrary compact Hermitian manifolds. This correspondence refers to moduli spaces of "universal holomorphic oriented pairs". Most of the classical moduli problems in complex geometry (e. g. holomorphic bundles with reductive structure groups, holomorphic pair…

Assume that all spaces and maps are localised at a fixed prime $p$. We study the possibility of generating a universal space $U(X)$ from a space $X$ which is universal in the category of homotopy associative, homotopy commutative H-spaces in the sense that any map f:X->Y to a homotopy associative, homotopy commutative …

In the first of these two lectures, I describe a gauge theory approach to understanding quantum knot invariants as Laurent polynomials in a complex variable q. The two main steps are to reinterpret three-dimensional Chern-Simons gauge theory in four dimensional terms and then to apply electric-magnetic duality. The var…

Prototype rules simplify multiclass classification in metric spaces, achieving consistency and reduced complexity.

Graph complex acts on Poisson bi-vectors, producing universal cocycles.

Study on scalar curvature bounds and manifold topological complexity.

Global group laws connect equivariant bordism rings to formal group laws.

Proves a formula for push-forward of polynomial Chern forms in universal vector bundles.

Constructs universal local deformations for curves and differential forms.

In this paper, we establish universal inequalities for eigenvalues of the clamped plate problem on compact submanifolds of Euclidean spaces, of spheres and of real, complex and quaternionic projective spaces. We also prove similar results for the biharmonic operator on domains of Riemannian manifolds admitting spherica…