相关论文: Manifolds, Structures Categorically

We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…

On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…

In this paper we outline a setup for Homological Mirror Symmetry for manifolds of general type. Both Physics and Categorical perspectives are considered.

Geometric symmetry induces symmetries of function spaces, and the latter yields a clue to global analysis via representation theory. In this note we summarize recent developments on the general theory about how geometric conditions affect…

We construct an explicit representation of the algebra of local diffeomorphisms of a manifold with realistic dimensions. This is achieved in the setting of a general approach to the (quantum) dynamics of a physical system which is…

On a generalized complex manifold there is an associated definition of a generalized holomorphic bundle, introduced by Gualtieri. This notion in the case of an ordinary complex structure yields an object which we call a co-Higgs bundle and…

The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of…

The twistor construction for Riemannian manifolds is extended to the case of manifolds endowed with generalized metrics (in the sense of generalized geometry \`a la Hitchin). The generalized twistor space associated to such a manifold is…

A description of physical reality in which wholeness is the foundation is discussed along with the motivation for such an attempt. As a possible mathematical framework within which a physical theory based on wholeness may be expressed,…

We will introduce formal frames of manifolds, which are a generalization of ordinary frames. Their fundamental properties are discussed. In particular, canonical forms are introduced, and torsions are defined in terms of them as a…

In this article ideas from Kit Fine's theory of arbitrary objects are applied to questions regarding mathematical structuralism. I discuss how sui generic mathematical structures can be viewed as generic systems of mathematical objects,…

The general concept of symmetry is realized in manifold ways in different realms of reality, such as plants, animals, minerals, mathematical objects or human artefacts in literature, fine arts and society. In order to arrive at a common…

Hyperspaces form a powerful tool in some branches of mathematics: lots of fractal and other geometric objects can be viewed as fixed points of some functions in suitable hyperspaces - as well as interesting classes of formal languages in…

This is the first paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In this paper, we lay the foundations for this study by introducing the…

To most mathematicians and computer scientists the word ``tree'' conjures up, in addition to the usual image, the image of a connected graph with no circuits. In the last few years various types of trees have been the subject of much…

Cofibration categories are a formalization of homotopy theory useful for dealing with homotopy colimits that exist on the level of models as colimits of cofibrant diagrams. In this paper, we deal with their enriched version. Our main result…

We consider a classical N. Steenrod's problem on realization of homology classes by images of the fundamental classes of manifolds. It is well-known that each integral homology class can be realized with some multiplicity as an image of the…

This article is dedicated to the investigation of difficulties involved in the understanding of the homomorphism concept. It doesn't restrict to group-theory but on the contrary raises the issue of developing teaching strategies aiming at…

Inspired by work of Borzellino and Brunsden, we generalize the notion of a submanifold identifying a natural and sufficiently general condition which guarantees that a subset of an (effective) orbifold carries itself a canonical induced…

An operator generalisation of the notion of geometric phase has been recently proposed purely based on physical grounds. Here we provide a mathematical foundation for its existence, while uncovering new geometrical structures in quantum…