Related papers: Generalized complex geometry
This is an expository paper, which provides a first introduction to geometric structures on $TM\oplus T^*M$. The paper contains definitions and characteristic properties of generalized complex, generalized Kaehler, generalized (normal,…
This paper uses a generalization of symplectic geometry, known as $n$-symplectic geometry and developed by Norris, to find observables on three-dimensional manifolds. It will be seen that for the cases considered, the $n$-symplectic…
We discuss the structure of "exceptional generalised geometry" (EGG), an extension of Hitchin's generalised geometry that provides a unified geometrical description of backgrounds in eleven-dimensional supergravity. On a d-dimensional…
In recent years, a close connection between supergravity, string effective actions and generalized geometry has been discovered that typically involves a doubling of geometric structures. We investigate this relation from the point of view…
We study symplectic forms on hypersurface algebroids. These are a broad generalization of the $b^{k}$-Poisson structures studied extensively by Miranda, Scott, and collaborators, and their geometry is intimately related to the group of…
Generalisations of geometry have emerged in various forms in the study of field theory and quantization. This mini-review focuses on the role of higher geometry in three selected physical applications. After motivating and describing some…
We develop a real-analytic framework, called perplex analysis, in which the complex, split-complex, and dual numbers arise as members of a single four-parameter family of two-dimensional commutative real algebras. Within this unified…
Derived brackets as introduced and studied by Kosmann-Schwarzbach and Voronov are a powerful tool for describing and understanding infinitesimal symmetry actions relevant in physics. Roytenberg and Weinstein showed that this continues to…
The basic idea of quantum complexity geometry is to endow the space of unitary matrices with a metric, engineered to make complex operators far from the origin, and simple operators near. By restricting our attention to a finite subgroup of…
Despite remarkable success in describing supergravity reductions and backgrounds, generalized geometry and the closely related exceptional field theory are still lacking a fundamental object of differential geometry, the Riemann tensor. We…
We study integrability of generalized almost contact structures, and find conditions under which the main associated maximal isotropic vector bundles form Lie bialgebroids. These conditions differentiate the concept of generalized contact…
We consider the problem of deforming simultaneously a pair of given structures. We show that such deformations are governed by an L-infinity algebra, which we construct explicitly. Our machinery is based on Th. Voronov's derived bracket…
We introduce linear Dirac and generalized complex structures on Cartan geometries and give criteria for Dirac subalgebras of $\frkg\ltimes\frkg^*$ representing Dirac structures on a Cartan geometry. We prove that there is a bijection…
In this note we give simple symplecticity conditions for implicit schemes in the linear case. We consider implicit maps on generic symplectic manifold and we introduce the concept of consistent implicit maps, to generalize the symplecticity…
We study higher-degree generalizations of symplectic groupoids, referred to as {\em multisymplectic groupoids}. Recalling that Poisson structures may be viewed as infinitesimal counterparts of symplectic groupoids, we describe "higher''…
A notion of general manifolds is introduced. It covers all usual manifolds in mathematics. Essentially, it is a way how to get a bigger 'fibration' over a site which locally coincides with a given one. An enrichment with generalized…
The aim of this paper to introduce the reader to a recent point of view on the Lipschitz classifications of complex singularities. It presents the complete classification of Lipschitz geometry of complex plane curves singularities and in…
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 construction of manifold structures and fundamental classes on the (compactified) moduli spaces appearing in Gromov-Witten theory is a long-standing problem. Up until recently, most successful approaches involved the imposition of…
We prove that Hitchin's generalized Kaehler structure on the moduli space of instantons over a compact, even generalized Kaehler four-manifold may be obtained by generalized Kaehler reduction, in analogy with the usual Kaehler case. The…