arXiv research

The closure conditions of the inexact exterior differential form and dual form (an equality to zero of differentials of these forms) can be treated as a definition of some differential-geometrical structure. Such a connection discloses the properties and specific features of the differential-geometrical structures. The…

Paper defines quasi-Strebel structures for meromorphic k-differentials and proves their existence.

Differential K-theory gets a $λ$-ring structure.

Tensoring $p$-weak differentiable structures preserves their properties.

Extends abelian differentials to log twisted differentials with spin and hyperelliptic structures.

New method recovers transportable DAG structures from different datasets.

It is known that the long line supports $2^{\aleph_1}$ many non-diffeomorphic differential structures. We show that the long plane supports a similar number of exotic differential structures, ie structures which are not merely diffeomorphic to the product of two structures on the factor spaces.

New contact structures defined on differentiable stacks.

Determines algebra structure of complex differential forms operators.

The paper constructs Levi flat structures using structure sheaves and differential complexes.

Lecture notes introduce differential geometry using sheaves and differential operators.

Global invariant for path structures and differential equations defined on torus.

New geometric Joyce structures on moduli spaces of quadratic differentials.

Different mathematical structures for calculus on sets.

Study non-formal pseudo-differential operators over formal ones.

Study uses Amari functors to investigate metric structures in gauge theories.

Researchers address the generation of differential invariants for geometric structures.

Proposes a differentiable structure learning framework for general binary data.

Abstract: Explains translating derived algebraic geometry results to derived differential geometry.

Study real logarithms of semi-simple matrices, focusing on differential structure.

Survey of geometry developments, including complex structures on surfaces.

The uniform structure on a differential space defined by a family of generators is considered.

Study of differential operators in PCS structures using contactifications.

This paper defines and examines the basic properties of noncommutative analogues of almost complex structures, integrable almost complex structures, holomorphic curvature, cohomology, and holomorphic sheaves. The starting point is a differential structure on a noncommutative algebra defined in terms of a differential g…

Survey on quadratic differentials in Teichmüller theory.

Novel method identifies structural differences between networks using structural equation models.

The study connects cubic differentials to convex RP^2-structures and their ends.

Defines algebraic structures in Lagrangian Floer cohomology using differential forms.

In this paper, we introduce a new concept so called harmonic complex structure by using harmonic theory for vector bundle-valued differential forms. It is a new structure intermediates between complex structure and Kähler structure. From differential geometric viewpoint, it is a natural generalization of Kähler structu…

In the background effective field theory of heterotic string theory, the Green-Schwarz anomaly cancellation mechanism plays a key role. Here we reinterpret it and its magnetic dual version in terms of differential twisted String- and differential twisted Fivebrane-structures that generalize the notion of Spin-structure…

According to the work of Kontsevich-Zorich, the invariant that classifies non-hyperelliptic connected components of the moduli spaces of Abelian differentials with prescribed singularities,is the parity of the spin structure. We show that for the moduli space of quadratic differentials, the spin structure is constant o…

The paper constructs a complex of differential operators on symplectic manifolds with metaplectic structures.

Survey explores cohomology's roles in applied math and sciences.

Variational approach to basic manifold structures.

Equivalence of second order differential operators in vector bundles studied.

We discuss relations between the para-CR structures and differential equations (both ODEs and PDEs of finite type).

What are called secondary characteristic classes in Chern-Weil theory are a refinement of ordinary characteristic classes of principal bundles from cohomology to differential cohomology. We consider the problem of refining the construction of secondary characteristic classes from cohomology sets to cocycle spaces; and …

We classify linear Nambu structures (which are generalized Poisson structures in Hamiltonian dynamics and which give rise to integrable differential forms and singular foliations), then give a linearization for Nambu structures anf integrable differential forms near a nondegenerate singular point.

Study of Cayley structures linked to differential equations.

Survey on symmetry in manifold structures.

Introduces Q-structures for mechanics using advanced geometry.

Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for the existence of a complete uniform differential structure on a given differenti…

We classify, up to diffeomorphism, all closed smooth manifolds homeomorphic to the complex projective $n$-space $\mathbb{C}\textbf{P}^n$, where $n=3$ and $4$. Let $M^{2n}$ be a closed smooth $2n$-manifold homotopy equivalent to $\mathbb{C}\textbf{P}^n$. We show that, up to diffeomorphism, $M^{6}$ has a unique different…

Defines new rho invariant for topological groups.

Subcartesian spaces follow Leibniz' rule, simplifying differential calculus.

This article provides a complete description of the differential Gerstenhaber algebras of all nilpotent complex structures on any real six-dimensional nilpotent algebra. As an application, we classify all pseudo-Kählerian complex structures on six-dimensional nilpotent algebras such that the differential Gerstenhaber a…

Differential calculus on metric spaces is contained in the algebraic study of normed groupoids with $δ$-structures. Algebraic study of normed groups endowed with dilatation structures is contained in the differential calculus on metric spaces. Thus all algebraic properties of the small world of normed groups with dilat…

We study variuos homological structures associated with Poisson algebra, the canonical differential complex for singular Poisson structure and the analogue of the star operator for such manifolds. Give the interpretation of the classical Koszul differential of exterior forms, as the supercommutator with some second ord…