Related papers: Gerbes on $G_2$ Manifolds

The purpose of this paper is to introduce Harvey-Lawson manifolds and review the construction of certain mirror dual Calabi-Yau submanifolds inside a G_2 manifold. More specifically, given a Harvey-Lawson manifold HL, we explain how to…

The goal of this paper is the construction of a compact manifold with G$_2$ holonomy and nodal singularities along circles using twisted connected sum method. This paper finds matching building blocks by solving the Calabi conjecture on…

Inspired by a string duality, we construct a deformation family for $G_2$-orbifolds given as total spaces of coassociative fibrations by ADE singularities over a closed and oriented smooth three-manifold $Q$. The deformations are…

Let $S$ be a closed surface of genus $g \geq 2$. We construct locally homogeneous geometric structures on closed 5-manifolds fibering over $S$, modeled on the two partial flag manifolds $\mathrm{Ein}^{2,3}$ and $\mathrm{Pho}^\times$ of the…

Let G be a Lie goup, let M and N be smooth connected G-manifolds, let f be a smooth G-map from M to N, and let P denote the fiber of f. Given a closed and equivariantly closed relative 2-form for f with integral periods, we construct the…

Let X be an Abelian surface and C a holomorphic curve in X representing a primitive homology class. The space of genus g curves in the class of C is g dimensional. We count the number of such curves that pass through g generic points and we…

Using an algebraic orbifold method, we present non-commutative aspects of $G_2$ structure of seven dimensional real manifolds. We first develop and solve the non commutativity parameter constraint equations defining $G_2$ manifold algebras.…

In the context of non-abelian gerbes we define a cubical version of categorical group 2-bundles with connection over a smooth manifold. We define their two-dimensional parallel transport, study its properties, and define non-abelian Wilson…

We construct geometrically a gerbe assigned to a connection on a principal SU(2)-bundle over an oriented closed 1-dimensional manifold. If the connection is given by the restriction of a connection on a bundle over a compact 2-manifold…

We give graphical presentations for the two quantum subgroups of type $G_2$. To do this we use a method of extending a tensor category by embedding the planar algebra of a $\otimes$-generating object into the graph planar algebra of this…

The topological classification of gerbes, as principal bundles with the structure group the projective unitary group of a complex Hilbert space, over a topological space $H$ is given by the third cohomology $\text{H}^3(H, \Bbb Z)$. When $H$…

Let G be a compact Lie group acting on a smooth manifold M. In this paper, we consider Meinrenken's G-equivariant bundle gerbe connections on M as objects in a 2-groupoid. We prove this 2-category is equivalent to the 2-groupoid of gerbe…

We study closures of GL_2(R)-orbits on the total space of the Hodge bundle over the moduli space of curves under the assumption that they are algebraic manifolds. We show that, in the generic stratum, such manifolds are the whole stratum,…

We explore a new direction in representation theory which comes from holomorphic gerbes on complex tori. The analogue of the theta group of a holomorphic line bundle on a (compact) complex torus is developed for gerbes in place of line…

This article constructs coassociative submanifolds in $G_2$-manifolds arising from Joyce's generalised Kummer construction. The novelty compared to previous constructions is that these submanifolds all lie within the critical region of the…

We define the notion of a parahoric group scheme $\mathcal G$ over a smooth projective curve, and formulate four conjectures on the structure of the stack of $\mathcal G$-bundles, which generalize to this case well-known results on…

Let A be a finite abelian group. We set up an algebraic framework for studying A-equivariant complex-orientable cohomology theories in terms of a suitable kind of equivariant formal groups. We compute the equivariant cohomology of many…

Let G be an affine reductive algebraic group over an algebraically closed field k. We determine the Picard group of the moduli stacks of principal G-bundles on any smooth projective curve over k.

In this note we identify two complex structures (one is given by algebraic geometry, the other by gauge theory) on the set of isomorphism classes of holomorphic bundles with section on a given compact complex manifold. In the case of line…

We study a novel type of braid groups on a closed orientable surface $\Sigma$. These are fundamental groups of certain manifolds that are hybrids between symmetric products and configuration spaces of points on $\Sigma$; a class of examples…