相关论文: The Geometry of Orbifolds via Lie Groupoids

This entry contains the core material of my habilitation thesis, soon to be officially submitted. It provides a self-contained presentation of the original results in this thesis, in addition to their detailed proofs. The motivation of…

This survey aims to provide a guide to the literature on topological 4-manifolds. Foundational theorems on 4-manifolds are stated, especially in the topological category. Precise references are given, with indications of the strategies…

This book is addressed to students, professors and researchers of geometry, who will find herein many interesting and original results. The originality of the book The Geometry of Homological Triangles consists in using the homology of…

This is a survey paper on Alegbraic Geometry over Lie Algebras

We propose a geometric integrator to numerically approximate the flow of Lie systems. The key is a novel procedure that integrates the Lie system on a Lie group intrinsically associated with a Lie system on a general manifold via a Lie…

In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.

In this paper we discuss about properties of lattices and its application in theoretical and algorithmic number theory. This result of Minkowski regarding the lattices initiated the subject of Geometry of Numbers, which uses geometry to…

We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which ``controls'' deformations of the structure bracket of the algebroid. We also have a closer look at various special cases…

We investigate the geometric and topological structure of equidistant decompositions of Riemannian manifolds.

In this paper we present a new procedure to obtain unitary and irreducible representations of Lie groups starting from the cotangent bundle of the group (the cotangent group). We discuss some applications of the construction in…

An idea to present a classical Lie group of positive dimension by generators and relations sounds dubious, but happens to be fruitful. The isometry groups of classical geometries admit elegant and useful presentations by generators and…

The geometric theory of Lie systems is used to establish integrability conditions for several systems of differential equations, in particular some Riccati equations and Ermakov systems. Many different integrability criteria in the…

We study the geometric and algebraic properties of the twisted Poisson structures on Lie algebroids, leading to a definition of their modular class and to an explicit determination of a representative of the modular class, in particular in…

In a previous paper, we introduce and study formal manifolds, which generalize smooth manifolds. In this paper, we establish the basic theory of formal Lie groups, which are group objects in the category of formal manifolds. In particular,…

The main purpose of this paper is to describe some published results and outline corresponding approaches which when applied to automorphism groups of algebras or groups establish that these groups are linear or non-linear.

In this paper we study three-dimensional orbifolds by 2-groups with a trivially-acting one-form symmetry group BK. These orbifolds have a global two-form symmetry, and so one expects that they decompose into (are equivalent to) a disjoint…

This is a survey of the theory of real trees and their applications.

The aim of the present paper is to provide a comprehensive introduction to some algebraic and geometric aspects of real representations of compact Lie groups, as well as some results concerning isotropy strata and restriction of invariants.

We survey some aspects of the theory of Hopf-Galois objects that may studied advantageously by using the language of cogroupoids. These are the notes for a series of lectures given at Cordoba University, may 2010. The lectures are part of…

These notes are devoted to explaining aspects of the mirror manifold problem that can be naturally understood from the point of view of topological field theory. Basically this involves studying the topological field theories made by…