Related papers: Constructions of generalized complex structures in…

In recent work N. Hitchin introduced the concept of "generalised geometry". The key feature of generalised structures is that that they can be acted on by both diffeomorphisms and 2-forms, the so-called $B$-fields. In this lecture, we give…

Generalized $(\kappa ,\mu )$ structures occur in dimension 3 only. In this dimension 3, only K-contact structures can occur as generalized Eta-Einstein. On closed manifolds, Eta-Einstein, K-contact structures which are not D-homothetic to…

Recently there has been an increasing interest in the study of generalized symmetries in dimensions higher than two. This has lead to the discovery of various manifestations of generalized symmetries, notably higher-group and non-invertible…

Concepts and techniques from the theory of G-structures of higher order are applied to the study of certain structures (volume forms, conformal structures, linear connections and projective structures) defined on a pseudo-Riemanniann…

In this paper, we review or introduce several differential structures on manifolds in the general setting of real and complex differential geometry, and apply this study to Teichm\"uller theory. We focus on bi-Lagrangian i.e. para-K\"ahler…

We describe a necessary and sufficient condition for a principal circle bundle over an even-dimensional manifold to carry an invariant contact structure. As a corollary it is shown that all circle bundles over a given base manifold carry an…

Observable structures of a topological field theory of AKSZ type are analyzed. From a double (or multiple) complex structure of observable algebras, new topological invariants are constructed. Especially, Donaldson polynomial invariants and…

This thesis develops the theory of bundle gerbes and examines a number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead…

We propose a generalization of small world networks, in which the reconnection of links is governed by a function that depends on the distance between the elements to be linked. An adequate choice of this function lets us control the…

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…

Generalized topological spaces in the sense of Cs\'{a}sz\'{a}r have two main features which distinguish them from typical topologies. First, these families of subsets are not closed under intersections. Second, we allow for the possibility…

Using the technique of quasi difference sets we characterize geometry and automorphisms of configurations which can be presented as a join of some others, in particular - which can be presented as series of cyclically inscribed copies of…

We define and analyze various generalizations of the punctual Hilbert scheme of the plane, associated to complex or real Lie algebras. Out of these, we construct new geometric structures on surfaces whose moduli spaces share multiple…

There are studied Lie groups considered as almost hypercomplex Hermitian-Norden manifolds, which are integrable and have the lowest dimension four. It is established a correspondence of the derived Lie algebras of types of invariant…

We point out that any stable generalized complex structure on a sphere bundle over a closed surface of genus at least two must be of constant type.

A parameterisation of generalised network clustering, in the form of four-motif prevalences, is presented. This involves three real parameters that are conditional on one- two- and three-motif prevalences. Interpretations of these real…

A notion of dual curve for pseudoholomorphic curves in 4--manifolds turns out to be possible only if the notion of almost complex structure structure is slightly generalized. The resulting structure is as easy (perhaps easier) to work with,…

On a complex symplectic manifold, we construct the stack of quantization-deformation modules, that is, (twisted) modules of microdifferential operators with an extra central parameter, a substitute to the lack of homogeneity. We also…

Jacobi sigma models are two-dimensional topological non-linear field theories which are associated with Jacobi structures. The latter can be considered as a generalization of Poisson structures. After reviewing the main properties and…

A generalization of classical theorems on the existence of sections of real, complex and quaternionic Stiefel manifolds is proved.