Related papers: Introducing Quaternionic Gerbes

In this PhD thesis, we have studied certain geometric structures over Lie groupoids and differentiable stacks. This thesis is based on the work [arXiv:2103.04560, arXiv:2012.08447, arXiv:2012.08442, arXiv:1907.00375]. In [arXiv:1907.00375],…

We study rationality properties of quadric surface bundles over the projective plane. We exhibit families of smooth projective complex fourfolds of this type over connected bases, containing both rational and non-rational fibers.

We establish relations between both the classical and the dual Garside structures of the braid group and the Burau representation. Using the classical structure, we formulate a non-vanishing criterion for the Burau representation of the…

We use pluriharmonic maps to study representations of fundamental groups of algebraic manifolds. This approach is functorial in the sense that the restriction of such a map to a fiber of a fibration remains pluriharmonic, and on this basis,…

The purpose of this paper is to describe certain natural 4-vector fields on quaternionic flag manifolds, which geometrically determine the Bruhat cell decomposition. This structure naturally descends from the symplectic group, where it is…

The definition and structure of hyperkahler structure preserving transformations (invariance group) for quaternionic structures have been recently studied and some preliminary results on the Euclidean case discussed. In this work we present…

This thesis reviews the theory of bundle gerbes and then examines the higher dimensional notion of a bundle 2-gerbe. The notion of a bundle 2-gerbe connection and 2-curving are introduced and it is shown that there is a class in…

We show that 4--dimensional conformal field theory is most naturally formulated on Kulkarni 4--folds, i. e. real 4--folds endowed with an integrable quaternionic structure. This leads to a formalism that parallels very closely that of…

We show that all spin groups of non-definite, quinary quadratic forms over a field with characteristic 0 can be represented as 2 by 2 matrices with entries in an associated quaternion algebra. Over local and global fields, we further study…

We propose a simple definition of a Born geometry in the framework of K\"unneth geometry. While superficially different, this new definition is equivalent to the known definitions in terms of para-quaternionic or generalized geometries. We…

We obtain a branched spherical CR structure on the complement of the figure eight knot with a given holonomy representation (called rho_2). There are essentially two boundary unipotent representations from the complement of the figure eight…

We discuss complex quaternionic manifolds, i.e., those that have holonomy $GL(n,\mathbb{H})U(1)$, which naturally arise via quaternionic Feix--Kaledin construction. We show that for a fixed c-projective class, any real analytic connection…

In this paper we suggest a definition for a C*-algebra attached to an injective morphism of some \'Etale groupoid. We take into account all the peculiarities of such objects and present some interesting relations with already well-known…

In this study, we try to semi-real quaternionic curves in the semi-Euclidean space E_2^4. Firstly, we introduce algebraic properties of semi-real quaternions. And then, we give some characterizations of semi-real quaternionic…

We view conformal surfaces in the 4--sphere as quaternionic holomorphic curves in quaternionic projective space. By constructing enveloping and osculating curves, we obtain new holomorphic curves in quaternionic projective space and thus…

We present a construction of a canonical G_2 structure on the unit sphere tangent bundle S_M of any given orientable Riemannian 4-manifold M. Such structure is never geometric or 1-flat, but seems full of other possibilities. We start by…

We introduce the concept of Spin^G-structure in a SO-bundle, where $G\subset U(V)$ is a compact Lie group containing $-id_V$. We study and classify $Spin^G(4)$-structures on 4-manifolds, we introduce the G-Monopole equations associated with…

In this paper we introduce a new and large family of configurations whose toric ideals possess quadratic Groebner bases. As an application, a generalization of algebras of Segre-Veronese type will be studied.

We discuss an unusual phenomenon in (integral) positive ternary quadratic forms. We also describe an interesting pairing of genera of ternary forms.

Quadric complexes are square complexes satisfying a certain combinatorial nonpositive curvature condition. These complexes generalize 2-dimensional CAT(0) cube complexes and are a square analog of systolic complexes. We introduce and study…