Related papers: Infinitesimal Automorphisms and Deformations of Pa…
BGG-sequences offer a uniform construction for invariant differential operators for a large class of geometric structures called parabolic geometries. For locally flat geometries, the resulting sequences are complexes, but in general the…
We provide an extension of the Gromov--Zimmer Embedding Theorem for Cartan geometries of [3] to tractor bundles carrying any invariant connection, including tractor connections and prolongation connections of first BGG operators for…
This article contributes to the relative BGG-machinery for parabolic geometries. Starting from a relative tractor bundle, this machinery constructs a sequence of differential operators that are naturally associated to the geometry in…
In this continuation of \cite{BDS}, we investigate the deformations of holomorphic Cartan geometries where the underlying complex manifold is allowed to move. The space of infinitesimal deformations of a flat holomorphic Cartan geometry is…
A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…
In a recent work it was shown that conformal Carroll geometries are canonically equipped with a null-tractor bundle generalizing the tractor bundle of conformal geometry. We here show that in the case of the conformal boundary of an…
BGG resolutions and generalized BGG resolutions from representation theory of semisimple Lie algebras have been generalized to sequences of invariant differential operators on manifolds endowed with a geometric structure belonging to the…
In this paper, we show that the infinitesimal Torelli theorem implies the existence of deformations of automorphisms. In the first part, we use Hodge theory and deformation theory to study the deformations of automorphisms of complex…
Automorphism groups are intrincate conjugacy invariants for subshifts, which can reveal important features of the dynamical structure of a shift action. One important case is the study of automorphism groups when the underlying subshift has…
For smooth manifolds equipped with various geometric structures, we construct complexes that replace the de Rham complex in providing an alternative fine resolution of the sheaf of locally constant functions. In case that the geometric…
It is outlined how deformations of field theoretical rigid symmetries can be constructed and classified by cohomological means in the extended antifield formalism. Special attention is devoted to deformations referring only to a subset of…
The realization of tractor bundles as associated bundles in conformal geometry is studied. It is shown that different natural choices of principal bundle with normal Cartan connection corresponding to a given conformal manifold can give…
We discuss some specializations of the frames of flat orthonormal frame bundles over geometries of indefinite signature, and the resulting symmetries of families of embedded Riemannian or pseudo-Riemannian geometries. The specializations…
We study infinitesimal deformations of autodual and hyper-holomorphic connections on complex vector bundles on hyper-K\"ahler manifolds of arbitrary dimension. In particular, we describe the DG Lie algebra controlling this deformation…
Introducing the deformation theory of holomorphic Cartan geometries, we compute infinitesimal automorphisms and infinitesimal deformations. We also prove the existence of a semi-universal deformation of a holomorphic Cartan geometry.
VB-groupoids and algebroids are vector bundle objects in the categories of Lie groupoids and Lie algebroids respectively, and they are related via the Lie functor. VB-groupoids and algebroids play a prominent role in Poisson and related…
In this paper, we prove that infinitesimal automorphisms of an involutive structure are smooth. For this, we build a regularity theory for sections of vector bundles over an involutive structure $(M,V)$ endowed with a connection compatible…
In the physics literature, Bilal--Fock--Kogan \cite{BFK} introduced the idea of parabolic reduced flat connections on a surface to give a geometric origin to $W$-algebras. In this paper, we combine these ideas with higher complex…
We present a new construction for Poisson transforms between vector bundle valued differential forms on homogeneous parabolic geometries and the corresponding Riemannian symmetric space, which can be described in terms of finite dimensional…
We prove a theorem relating the automorphism group of a Cartan geometry to the group on which the geometry is modeled: a component of the adjoint representation of the first embeds in the adjoint representation of the second. Consequences…