arXiv subjects

Ori Yudilevich

Publications and source records attributed to Ori Yudilevich.

4 recordsLinked to original sources

arXiv2020

Homogeneous G-structures

The theory of $G$-structures provides us with a unified framework for a large class of geometric structures, including symplectic, complex and Riemannian structures, as well as foliations and many others. Surprisingly, contact geometry - the "odd-dimensional counterpart" of symplectic geometry - does not fit naturally into this picture. In this paper, we introduce the notion of a homogeneous $G$-structure, which encompasses contact structures, as well as some other interesting examples that appear in the literature.

math.DG↗

arXiv2019

Lie Pseudogroups à la Cartan

We present a modern formulation of Élie Cartan's structure theory for Lie pseudogroups and prove a reduction theorem that clarifies the role of Cartan's systatic system. The paper is divided into three parts. In part one, using notions coming from the theory of Lie groupoids and algebroids, we introduce the framework of Cartan algebroids and realizations, structures that encode Cartan's structure equations and notion of a pseudogroup in normal form. In part two, we present a novel proof of Cartan's Second Fundamental Theorem, which states that any Lie pseudogroup is equivalent to a pseudogroup in normal form. In part three, we prove a new reduction theorem that states that, under suitable regularity conditions, a pseudogroup in normal form canonically reduces to a generalized pseudogroup of local solutions of a Lie-Pfaffian groupoid.

math.DG↗

arXiv2018

On the Inner Automorphisms of a Singular Foliation

A singular foliation in the sense of Androulidakis and Skandalis is an involutive and locally finitely generated module of compactly supported vector fields on a manifold. An automorphism of a singular foliation is a diffeomorphism that preserves the module. In this note, we give an alternative proof of the (surprisingly non-trivial) fundamental fact that the time-one flow of an element of a singular foliation (i.e. its exponential) is an automorphism of the singular foliation.

math.DG↗

arXiv2015

The Role of the Jacobi Identity in Solving the Maurer-Cartan Structure Equation

We describe a method for solving the Maurer-Cartan structure equation associated with a Lie algebra that isolates the role of the Jacobi identity as an obstruction to integration. We show that the method naturally adapts to two other interesting situations: local symplectic realizations of Poisson structures, in which case our method sheds light on the role of the Poisson condition as an obstruction to realization; and the Maurer-Cartan structure equation associated with a Lie algebroid, in which case we obtain an explicit formula for a solution to the equation which generalizes the well known formula in the case of Lie algebras.

math.DG↗