相关论文: The Geometry of Orbifolds via Lie Groupoids

We study topological properties of the graph topology.

The aim of this note is to prove the algebraic geometry analogue of the Invariant tubular neighborhood theorem which concerns the actions of compact Lie groups on smooth manifolds.

Necessary or sufficient conditions are presented for the existence of various types of actions of Lie groups and Lie algebras on manifolds.

The use of double groupoids and their associated double Lie algebroids and characteristic distributions is proposed for the description and analysis of continuous media that carry two different constitutive or geometric structures. Various…

The main theorem states that any complete connected Riemannian manifold of bounded geometry can be isometrically realized as a leaf with trivial holonomy in a compact Riemannian foliated space.

Three-dimensional almost contact B-metric manifolds are constructed by a three-parametric family of Lie groups. It is established the class of the investigated manifolds which has an important geometrical interpretation. It is determined…

Torus orbifolds are topological generalization of symplectic toric orbifolds. We give a construction of smooth orbifolds with torus actions whose boundary is a disjoint union of torus orbifolds using toric topological method. As a result,…

The goal of this paper is to experiment new math concepts and theories, especially if they run counter to the classical ones. To prove that contradiction is not a catastrophe, and to learn to handle it in an (un)usual way. To transform the…

We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.

In the paper we study the algebroid A of the groupoid of partially invertible elements over the lattice of orthogonal projections of a $W^*$-algebra. In particular the complex analytic manifold structure of these objects is investigated.…

Orbifold groupoids have been recently widely used to represent both effective and ineffective orbifolds. We show that every orbifold groupoid can be faithfully represented on a continuous family of finite dimensional Hilbert spaces. As a…

The main goal of this thesis is to develop the integration theory of curved homotopy Lie algebras. In the first chapter, we develop the operadic calculus needed: we encode non-necessarily conilpotent coalgebras with operads and introduce…

It is well-known that reduced smooth orbifolds and proper effective foliation Lie groupoids form equivalent categories. However, for certain recent lines of research, equivalence of categories is not sufficient. We propose a notion of maps…

Let M be a manifold, and G a Lie group which satisfies the unique extension property. An (M,G) manifold N is a manifold endowed with an atlas (U_i,f_i) where f_i is a diffeomorphism between U_i and an open set of M such that the coordinates…

This work represents a PhD thesis concerning three main topics. The first one deals with the study and applications of Lie systems with compatible geometric structures, e.g. symplectic, Poisson, Dirac, Jacobi, among others. Many new Lie…

In this paper, we study geometric properties of quotient spaces of proper Lie groupoids. First, we construct a natural stratification on such spaces using an extension of the slice theorem for proper Lie groupoids of Weinstein and Zung.…

We survey the concept of multiplicativity from its initial appearance in the theory of Poisson-Lie groups to the far-reaching generalizations, for multivectors and differential forms in the geometry and the generalized geometry of Lie…

We give an up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds. We also mention some of their applications to time-dependent mechanics.

The purpose of this paper is to present projective geometry in a synthetic, visual and intuitive style through the central notion of harmonicity which leads to harmonic curves. This presentation includes new results, unpublished proofs of…

In this work we introduce the concepts of linguistic transformation, linguistic loop and semantic deficit. By exploiting Lie group theoretical and geometric techniques, we define invariants that capture the structural properties of a whole…