arXiv research

New insights into Khovanov homology complexity and topological structure.

Algorithm finds characteristic maps over complex shapes.

CR embeddings in complex spaces for specific Lie groups.

Wedge Sampling improves tensor completion with nearly-linear sample complexity.

The study finds minimal hypersurfaces in wedge-shaped manifolds with boundary.

Novel analysis of neural networks using geometric algebra and convex optimization.

Curvature estimate for stable free boundary minimal hypersurfaces in wedge-shaped manifolds.

Proves Khovanov homology has no torsion for bipartite circle graphs.

Discrete exterior calculus shows natural properties of wedge product and averaging.

Flat minimal hypersurfaces found in wedge-shaped domains.

Paper proves inequality for capillary hypersurfaces in a wedge.

Given a pair of (real or complex) Lie algebroid structures on a vector bundle $A$ (over $M$) and its dual $A^*$, and a line bundle $\module$ such that $\module\otimes\module=(\wedge^{\TOP} A^*\otimes\wedge^{\TOP} T^*M)$, there exist two canonically defined differential operators $\bdees$ and $\bdel$ on $\sections{\wedg…

We study the spectrum and heat kernel of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold degenerating to a manifold with wedge singularities. Provided the Hodge Laplacians in the fibers of the wedge have an appropriate spectral gap, we give uniform constructions of the resolvent and heat ker…

Study on scalar curvature in wedge spaces with existence and obstruction results.

Bordifications of hyperplane arrangements yield complexes with homotopy type of wedges of spheres.

We characterize N=1 vacua of type II theories in terms of generalized complex structure on the internal manifold M. The structure group of T(M) + T*(M) being SU(3) x SU(3) implies the existence of two pure spinors Phi_1 and Phi_2. The conditions for preserving N=1 supersymmetry turn out to be simple generalizations of …

Paper equates torsions on wedge singularities.

This paper extends Witten's holomorphic Morse inequalities to singular spaces.

Consider a financial market in which an agent trades with utility-induced restrictions on wealth. By introducing a general convex-analytic framework which includes the class of umbrella wedges in certain Riesz spaces and faces of convex sets (consisting of probability measures), together with a duality theory for polar…

This is the first paper in a series to develop a linear and nonlinear theory for elliptic and parabolic equations on Kähler varieties with mild singularities. Donaldson has established a Schauder estimate for linear and complex Monge-Ampère equations when the background Kähler metrics on $\mathbb{C}^n$ have cone singul…

We show that the disk complex of a genus $g>1$ Heegaard surface for the 3-sphere is homotopy equivalent to a wedge of $(2g-2)$-dimensional spheres. This implies that genus $g>1$ Heegaard surfaces for the 3-sphere are topologically minimal with index $2g-1$.

Geometrodynamics derived from Riemannian manifolds using geospin matrix.

Improved reinforcement learning for environments with distributional shifts.

A fake wedge is a diagram of spaces K <- A -> C whose double mapping cylinder is contractible. The terminology stems from the special case A = K v C with maps given by the projections. In this paper, we study the homotopy type of the moduli space D(K,C) of fake wedges on K and C. We formulate two conjectures concerning…

Let $(X,ω)$ be an $n$-dimensional compact Kähler manifold. We study degenerate complex Hessian equations of the form $(ω+dd^c\varphi)^m\wedge ω^{n-m}=F(x,\varphi)ω^n.$ Under some natural conditions on $F$, this equation has a unique continuous solution. When $(X,ω)$ is rational homogeneous we further show that the solu…

This paper classifies commutativity spaces for 3-manifold groups.

The study proves a theorem on Riemannian manifolds for wedge products of weakly convergent differential forms.

Let $Σ$ be a compact immersed stable capillary hypersurface in a wedge bounded by two hyperplanes in $\mathbb R^{n+1}$. Suppose that $Σ$ meets those two hyperplanes in constant contact angles and is disjoint from the edge of the wedge. It is proved that if $\partial Σ$ is embedded for $n=2$, or if $\partialΣ$ is convex…

Examines how irreducibility and rigidity affect digital images.

Let $(X,ω)$ be a compact Kähler manifold of dimension $n$, and fix $1\leq m\leq n.$ We prove that the complex Hessian equation $(ω+dd^c\varphi)^m\wedge ω^{n-m}=fω^n$, with $0<f\in \mathcal{C}^{\infty}(X)$ has a smooth admissible solution $\varphi\in \mathcal{C}^{\infty}(X)$. This was previously known to hold when $(X,…

A discrete (finite-difference) analogue of differential forms is considered, defined on simplicial complexes, including triangulations of continuous manifolds. Various operations are explicitly defined on these forms, including exterior derivative and exterior product. The latter one is non-associative. Instead, as ant…

We discuss the Ricci-flat `model metrics' on $\mathbb{C}^2$ with cone singularities along the conic $\{zw=1\}$ constructed by Donaldson using the Gibbons-Hawking ansatz over wedges in $\mathbb{R}^3$. In particular we describe their asymptotic behavior at infinity and compute their energies.

We show that the complex of free factors of a free group of rank n > 1 is homotopy equivalent to a wedge of spheres of dimension n-2. We also prove that for n > 1, the complement of (unreduced) Outer space in the free splitting complex is homotopy equivalent to the complex of free factor systems and moreover is (n-2)-c…

Query2box embeds complex queries as boxes to handle logical operations in large KGs.

Study anisotropic capillary surfaces in a wedge using generalized Minkowski norms.

We study the interplay among Wall's $D(2)$ problem, normal generation conjecture (the Wiegold Conjecture) of perfect groups and Swan's problem on partial Euler characteristic and deficiency of groups. In particular, for a 3-dimensional complex $X$ of cohomological dimension 2 with a finite fundamental group, assuming t…

We present some results supporting the Iwase-Sakai conjecture about coincidence of the topological complexity $TC(X)$ and monoidal topological complexity $TC^M(X)$. Using these results we provide lower and upper bounds for the topological complexity of the wedge $X\vee Y$. We use these bounds to give a counterexample t…

We introduce the C++ library Wedge, based on GiNaC, for symbolic computations in differential geometry. We show how Wedge makes it possible to use the language C++ to perform such computations, and illustrate some advantages of this approach with explicit examples. In particular, we describe a short program to determin…

Study contextual online pricing with biased offline data, achieving optimal regret bounds.

We study the character of the infinite wedge projective representation of the algebra of differential operators on the circle. We prove quasi-modularity of this character and also compute certain generating functions for traces of differential operators which we call correlation functions. These correlation functions a…

Johnson has defined a surjective homomorphism from the Torelli subgroup of the mapping class group of the surface of genus $g$ with one boundary component to $\wedge^3 H$, the third exterior product of the homology of the surface. Morita then extended Johnson's homomorphism to a homomorphism from the entire mapping cla…

The paper proves a comparison principle for complex Monge-Ampère flows and solves a uniqueness problem.

In this note we consider a heat trace expansion on a manifold with wedge-like singularity. We show that there are two terms in the expansion that contain information about the presence of the singularity, namely the logarithmic term $ct^{-1/2}\log t$ and the half power term $bt^{-1/2}$. We also give a geometric express…

It was proven by González-Meneses, Manchón and Silvero that the extreme Khovanov homology of a link diagram is isomorphic to the reduced (co)homology of the independence simplicial complex obtained from a bipartite circle graph constructed from the diagram. In this paper we conjecture that this simplicial complex is al…

Decomposes elements in multiplicative multivectors and relates to Lie algebroid cohomology.

New internal symmetry found for Lie pair algebra.

Study shows physical drift affects put-call parity enforcement, not just option payoffs.

We define quantum exterior product wedge_h and quantum exterior differential d_h on Poisson manifolds (of which symplectic manifolds are an important class of examples). Quantum de Rham cohomology, which is a deformation quantization of de Rham cohomology, is defined as the cohomology of d_h. We also define quantum Dol…