arXiv research

Defines constraint tensor for null hypersurfaces, providing explicit geometry.

Proves elliptic operator images are closed on Hilbert bundles.

Given a finitely generated and projective Lie-Rinehart algebra, we show that there is a continuous homomorphism of complete commutative Hopf algebroids between the completion of the finite dual of its universal enveloping Hopf algebroid and the associated convolution algebra. The topological Hopf algebroid structure of…

Algebras of smooth functions help reconstruct bulk topological types.

We create Resthetikhin-Turaev topological invariants of closed orientable three-manifolds from the quantum supergroup U_q(osp(1|2n)) at certain even roots of unity. To construct the invariants we develop tensor product theorems for finite dimensional modules of U_q(osp(1|2n)) at roots of unity.

The paper studies algebraic structures related to quantum groups.

Proves existence of maximizers for eigenvalue optimization on manifolds.

The tensor-tensor product (t-product) [M. E. Kilmer and C. D. Martin, 2011] is a natural generalization of matrix multiplication. Based on t-product, many operations on matrix can be extended to tensor cases, including tensor SVD, tensor spectral norm, tensor nuclear norm [C. Lu, et al., 2018] and many others. The line…

The main goal of this paper is to study the geometric structures associated with the representation of tensors in subspace based formats. To do this we use a property of the so-called minimal subspaces which allows us to describe the tensor representation by means of a rooted tree. By using the tree structure and the d…

The paper defines and analyzes curvature tensors on super twisted product spaces.

Study of monodromy and vanishing cycles for complete intersection curves.

Graphical notation simplifies tensor operations and decompositions.

We define the Bianchi-Massey tensor of a topological space X to be a linear map from a subquotient of the fourth tensor power of H*(X). We then prove that if M is a closed (n-1)-connected manifold of dimension at most 5n-3 (and n > 1) then its rational homotopy type is determined by its cohomology algebra and Bianchi-M…

Killing tensors on reducible spaces are reducible, except for special cases.

The study examines conditions for weak nearly cosymplectic manifolds to split into products.

The charged Nariai spacetimes are the exact solutions of Einstein-Maxwell field equations with positive cosmological constant and such a spacetime is the direct topological product of a $2$-dimentional de-Sitter spacetime with a round $2$-sphere of constant radius. The present paper deals with the investigation of curv…

Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering, the most abstract reaches of theoretical physics has spawned topological models ha…

Paper studies pseudo-projective tensors on warped products.

Explores tensor products in hyperdimensional computing.

Introduces tensor product for quiver representations and applies to stable bundles and character varieties.

Some invariant tensors in two Naveira classes of Riemannian product manifolds are considered. These tensors are related with natural connections, i.e. linear connections preserving the Riemannian metric and the product structure.

Properties of pairs of product conjugate connections are stated with a special view towards the integrability of the given almost product structure. We define the analogous in product geometry of the structural and the virtual tensors from the Hermitian geometry and express the product conjugate connections in terms of…

Defines tensor products for A-infinity structures using diagonals.

The study extends Jacobi-orthogonality to indefinite scalar product spaces.

Defines semi-symmetric metric connection on super warped products.

The main goal of this paper is to extend the so-called Dirac-Frenkel Variational Principle in the framework of tensor Banach spaces. To this end we observe that a tensor product of normed spaces can be described as a union of disjoint connected components. Then we show that each of these connected components, composed …

Paper introduces topological eigenvalue theorems for tensor analysis in multi-modal data.

The paper studies special warped products with a specific connection on super Riemannian manifolds.

Study on the topology of tensorial bodies, showing they are homeomorphic to a product space.

Paper introduces tensor product of quandles for knot classification.

Warped product manifolds with p-dimensional base, p=1,2, satisfy some curvature conditions of pseudosymmetry type. These conditions are formed from the metric tensor g, the Riemann-Christoffel curvature tensor R, the Ricci tensor S and the Weyl conformal curvature C of the considered manifolds. The main result of the p…

We prove that the category of $\mathbb{Z}_2 ^n$-manifolds has all finite products. Further, we show that a $\mathbb{Z}_2 ^n$-manifold (resp., a $\mathbb{Z}_2 ^n$-morphism) can be reconstructed from its algebra of global $\mathbb{Z}_2 ^n$-functions (resp., from its algebra morphism between global $\mathbb{Z}_2 ^n$-funct…

We present two formulas for Chern classes of the tensor product of two vector bundles. In the first formula we consider a matrix containing Chern classes of the first bundle and we take a polynomial of this matrix with Chern classes of the second bundle as coefficients. The determinant of this expression equals the Che…

New spectral sequence connects to topological Hochschild homology.

Generalizes warped product submersion to conformal case.

Study of group orderability using tensor and exterior squares.

In this paper, we consider the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is based on the recently proposed tensor-tensor product (or t-product). Induced by the t-product, we first rigorously deduce the tensor sp…

Geometrically, tensors of fixed rank form a minimal submanifold.

A new method reduces the complexity of tensor products from cubic to quadratic, improving both speed and accuracy.

We prove explicit formulas for Chern classes of tensor products of vector bundles, with coefficients given by certain universal polynomials in the ranks of the two bundles.

Study on properties of tangential hypersurfaces in product-like manifolds.

The class of the Riemannian almost product manifolds with nonintegrable structure is considered. Some identities for curvature tensor as certain invariant tensors and quantities are obtained.

Explicit formulas for the $G_2$-components of the Riemannian curvature tensor on a manifold with a $G_2$ structure are given in terms of Ricci contractions. We define a conformally invariant Ricci-type tensor that determines the 27-dimensional part of the Weyl tensor and show that its vanishing on compact $G_2$ manifol…

New method improves sales forecasting accuracy using tensor factorization.

MCCA extracts shared structure from multiple tensor datasets.

We study the Kasparov product on (possibly non-compact and incomplete) Riemannian manifolds. Specifically, we show on a submersion of Riemannian manifolds that the tensor sum of a regular vertically elliptic operator on the total space and an elliptic operator on the base space represents the Kasparov product of the co…

Holomorphic tensors on algebraic cones are invariant under certain group actions.

In this paper we give an example of a linear group such that its tensor square is not linear. Also, we formulate some sufficient conditions for the linearity of non-abelian tensor products $G \otimes H$ and tensor squares $G \otimes G$. Using these results we prove that tensor squares of some groups with one relation a…