相关论文: Aspects of the theory of infinite dimensional mani…

This survey is about the fundamentals of the theory of finite dimensional Lie groups over the field of real numbers. The notion of the tangent space of a manifold at a point is considered to be defined via the well known chart and vector…

A set of coordinates in the non parametric loop-space is introduced. We show that these coordinates transform under infinite dimensional linear representations of the diffeomorphism group. An extension of the group of loops in terms of…

In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of…

Let $M$ be any $n$ dimensional smooth manifold and $PM$ be the space of all smooth paths, then we showed that $PM$ is a smooth manifold modelled over a complete normable space. We discussed many geometric structure on Path spaces and its…

Given the interest in relating the large $N$ limit of SU(N) to groups of area-preserving diffeomorphisms, we consider the topologies of these groups and show that both in terms of homology and homotopy, they are extremely different. Similar…

We describe recent links between two topics: geometric structures on manifolds in the sense of Ehresmann and Thurston, and dynamics "at infinity" for representations of discrete groups into Lie groups.

Mapping spaces of supermanifolds are usually thought as exclusively in functorial terms (i.e. trough the Grothendieck functor of points). In this work we provide a geometric description of such mapping spaces in terms of…

In this paper, we introduce the notion of a super tangent bundle of a manifold, and extend the basic notions of differential geometry such as differential forms, exterior derivation, connection, metric and divergence on manifolds that…

This work serves as an opening and basis of an ongoing program investigating topological and geometric aspects of the moduli space of smooth fiberings on a manifold. The present paper focuses on the algebraic and differential topology of…

Chern-Weil and Chern-Simons theory extend to certain infinite-rank bundles that appear in mathematical physics. We discuss what is known of the invariant theory of the corresponding infinite-dimensional Lie groups. We use these techniques…

This work aims to define the concept of manifold, which has a very important place in the topology, on digital images. So, a general perspective is provided for two and three-dimensional imaging studies on digital curves and digital…

We study how the notion of tangent space can be extended from smooth manifolds to diffeological spaces, which are generalizations of smooth manifolds that include singular spaces and infinite-dimensional spaces. We focus on two definitions.…

This article analyzes the interplay between symplectic geometry in dimension four and the invariants for smooth four-manifolds constructed using holomorphic triangles introduced in math.SG/0110169. Specifically, we establish a non-vanishing…

Complete sets of bases of differential invariants, operators of invariant differentiation and Lie determinants of continuous transformation groups acting on the real plane are constructed. As a necessary preliminary, realizations of…

We discuss the Euclidean limit of hyperbolic SU(2)-monopoles, framed at infinity, from the point of view of pluricomplex geometry. More generally, we discuss the geometry of hypercomplex manifolds arising as limits of pluricomplex…

By studying connectedness at infinity of systolic groups we distinguish them from some other classes of groups, in particular from the fundamental groups of manifolds covered by euclidean space of dimension at least three. We also study…

We use differential forms on loop spaces to prove that the fundamental group of certain geometric transformation groups is infinite. Examples include both finite and infinite dimensional Lie groups. The finite dimensional examples are the…

An algebraic approach is developed to define and study infinite dimensional grassmannians. Using this approach a quantum deformation is obtained for both the ind-variety union of all finite dimensional grassmannians, and the Sato…

This short review is devoted to measures on infinite dimensional spaces. We start by discussing product measures and projective techniques. Special attention is paid to measures on linear spaces, and in particular to Gaussian measures.…

The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of…