arXiv research

Clarifies global structure of Stokes-Dirac structures on manifolds.

We show that every paracomplex space form is locally isometric to a modified Riemannian extension and give necessary and sufficient conditions so that a modified Riemannian extension is Einstein. We exhibit Riemannian extension Osserman manifolds of signature (3,3) whose Jacobi operators have non-trivial Jordan normal …

Geometric U-folds explained in 4D supergravity.

Study flat conical surfaces' Laplacian determinants, showing differences in holonomy.

Quantization of a Lagrangian field system essentially depends on its degeneracy and implies its BRST extension defined by sets of non-trivial Noether and higher-stage Noether identities. However, one meets a problem how to select trivial and non-trivial higher-stage Noether identities. We show that, under certain condi…

Quandles with involutions that satisfy certain conditions, called good involutions, can be used to color non-orientable surface-knots. We use subgroups of signed permutation matrices to construct non-trivial good involutions on extensions of odd order dihedral quandles. For the smallest example of order 6 that is an ex…

We study rank $1$ flat bundles over solvmanifolds whose cohomologies are non-trivial. By using Hodge theoretical properties for all topologically trivial rank $1$ flat bundles, we represent the structure theorem of Kähler solvmanifolds as extensions of Hasegawa's result and Benson-Gordon's result for nilmanifolds.

Quandle 2-cocycles yield invariant values for knots under certain algebraic conditions.

The purpose of this paper is to show how central extensions of (possibly infinite-dimensional) Lie algebras integrate to central extensions of étale Lie 2-groups. In finite dimensions, central extensions of Lie algebras integrate to central extensions of Lie groups, a fact which is due to the vanishing of π_2 for each …

The quandle homology theory is generalized to the case when the coefficient groups admit the structure of Alexander quandles, by including an action of the infinite cyclic group in the boundary operator. Theories of Alexander extensions of quandles in relation to low dimensional cocycles are developed in parallel to gr…

We describe natural abelian extensions of the Lie algebra $\aut(P)$ of infinitesimal automorphisms of a principal bundle over a compact manifold $M$ and discuss their integrability to corresponding Lie group extensions. Already the case of a trivial bundle $P = M \times K$ is quite interesting. In this case, we show th…

We give sharp sectional curvature estimates for complete immersed cylindrically bounded $m$-submanifolds $φ:M\to N\times\mathbb{R}^{\ell}$, $n+\ell\leq 2m-1$ provided that either $φ$ is proper with the second fundamental form with certain controlled growth or $M$ has scalar curvature with strong quadratic decay. This l…

Compact groups with polynomial growth have specific embeddings.

EM algorithm converges to global max in latent Gaussian tree models.

Unique 3-balls in S^4 can be non-isotopic.

Research characterizes traces of Sobolev mappings into manifolds, identifying analytical obstructions and proving surjectivity under certain conditions.

New smooth 2-group extensions from bundle gerbes on manifolds.

Survey of TreeLSTM models for transductions.

Constructs special Kähler structures on Lie groups.

The paper studies automorphisms of pure braid groups and their properties.

We establish that, for every hyperbolic orbifold of type (2, q, $\infty$) and for every orbifold of type (2, 3, 4g+2), the geodesic flow on the unit tangent bundle is left-handed. This implies that the link formed by every collection of periodic orbits (i) bounds a Birkhoff section for the geodesic flow, and (ii) is a …

This paper, the third in a series of eight introduces some of the basic concepts of the theory of extensors needed for our formulation of the differential geometry of smooth manifolds . Key notions such as the extension and generalization operators of a given linear operator (a (1,1)-extensor) acting on a real vector s…

Improves music composition with user-defined constraints using continuous time models.

Bayesian approach generalizes ADMM for federated learning.

Researchers extend differential expansion to links using special framing.

A fast spectral algorithm detects community structure in evolving graphs.

We give an extension of Fox's formula of the Alexander polynomial for double branched covers over the three-sphere. Our formula provides the Reidemeister torsion of a double branched cover along a knot for a non-trivial one dimensional representation by the product of two factors derived from the knot group. One of the…

The fundamental group of a Riemannian manifold with $δ$-pinched negative curvature, $δ>1/4$, cannot be the fundamental group of a quasicompact Kähler manifold. The proof also implies that a non-uniform lattice in $F_{4(-20)}$ cannot be the fundamental group of a quasicompact Kähler manifold. We also construct examples …

Let Σ_g be a closed orientable surface let Diff_0(Σ_g; area) be the identity component of the group of area-preserving diffeomorphisms of Σ_g. In this work we present an extension of Gambaudo-Ghys construction to the case of a closed hyperbolic surface Σ_g, i.e. we show that every non-trivial homogeneous quasi-morphism…

We classify the Markov traces factoring through the Birman-Wenzl-Murakami (BMW) algebras. For this purpose, we define a common `cover' for the two variations of the BMW-algebra originating from the quantum orthogonal/symplectic duality, which are responsible for the so-called `Dubrovnik' variation of the Kauffman polyn…

Surveying methods to create spaces with non-trivial self covers.

Virtual knot theory is a generalization (discovered by the author in 1996) of knot theory to the study of all oriented Gauss codes. (Classical knot theory is a study of planar Gauss codes.) Graph theory studies non-planar graphs via graphical diagrams with virtual crossings. Virtual knot theory studies non-planar Gauss…

Study shows non-trivial knot Floer homology for specific knots.

This paper studies quandles with one non-trivial column and their properties.

Develops a hybrid model for text summarization.

We say that a graph is intrinsically non-trivial if every spatial embedding of the graph contains a non-trivial spatial subgraph. We prove that an intrinsically non-trivial graph is intrinsically linked, namely every spatial embedding of the graph contains a non-splittable 2-component link. We also show that there exis…

This paper deals with the enumeration of the higher order non-trivial compositions of the differential operations and the directional derivative in the space $R^n$ ($n \geq 3$). We present the recurrences for a counting the higher order non-trivial compositions.

New methods found persistent tangles in knots.

The paper explores non-trivial welded knots and ribbon torus-knots, proving their existence.

Characterizes G2-structures on Lie algebras with non-trivial center.

New knots found with non-trivial Steenrod operations on Khovanov homology.

New Jordan Floer homology shows every curve inscribes every isosceles trapezoid.

Asymptotically harmonic manifolds are simply connected complete Riemannian manifolds without conjugate points such that all horospheres have the same constant mean curvature $h$. In this article we present results for harmonic functions on rank one asymptotically harmonic manifolds $X$ with mild curvature boundedness c…

Non-trivial conservation law found for a specific system.

Classifies charge-3 monopoles with symmetry, identifying new spectral curves.

Stability of Khovanov homotopy types of torus links as m increases.

Study calculates non-trivial link cohomologies and applies to branched double covers.

Proof that band sums of tight fibered knots result in non-tight fibered knots.