Related papers: Orbifold Biquotients of SU(3)
We develop a general theory of 3-dimensional ``orbifold completion'', to describe (generalised) orbifolds of topological quantum field theories as well as all their defects. Given a semistrict 3-category $\mathcal{T}$ with adjoints for all…
The correlation functions of supersymmetric gauge theories on a four-manifold X can sometimes be expressed in terms of topological invariants of X. We show how the existence of superconformal fixed points in the gauge theory can provide…
We elaborate on the construction of de Sitter solutions from IIA orientifolds of SU(3)-structure manifolds that solve the 10-dimensional equations of motion at tree-level in the approximation of smeared sources. First we classify geometries…
We study conditions under which the Hausdorff quasi-uniformity ${\mathcal U}_H$ of a quasi-uniform space $(X,{\mathcal U})$ on the set ${\mathcal P}_0(X)$ of the nonempty subsets of $X$ is bicomplete. Indeed we present an explicit method to…
This is the first part of a series of papers where we compute Euler characteristics, signatures, elliptic genera, and a number of other invariants of smooth manifolds that admit Riemannian metrics with positive sectional curvature and large…
A new orientifold of Type-IIB theory on $K3$ is constructed that has $N=1$ supersymmetry in six dimensions. The orientifold symmetry consists of a $Z_2$ involution of $K3$ combined with orientation-reversal on the worldsheet. The…
A complete 5-dimensional SU(5) unified theory is constructed which, on compactification on the orbifold with two different Z_2's (Z_2 and Z_2'), yields the minimal supersymmetric standard model. The orbifold accomplishes SU(5) gauge…
Smale-Barden manifolds are simply-connected closed 5-manifolds. It is an important and difficult question to decide when a Smale-Barden manifold admits a Sasakian or a K-contact structure. The known constructions of Sasakian and K-contact…
``An orbifold is a space which is locally modeled on the quotient of a vector space by a finite group.'' This sentence is so easily said or written that more than one person has missed some of the subtleties hidden by orbifolds. Orbifolds…
The object of investigations are almost contact B-metric structures on 3-dimensional Lie groups considered as smooth manifolds. There are established the existence and some geometric characteristics of these manifolds in all basic classes.…
When considered as submanifolds of Euclidean space, the Riemannian geometry of the round sphere and the Clifford torus may be formulated in terms of Poisson algebraic expressions involving the embedding coordinates, and a central object is…
This note gives a uniform, self-contained, and fairly direct approach to a variety of obstruction-theoretic problems on 8-manifolds. We give necessary and sufficient cohomological critera for the existence of almost complex and almost…
Using recently developed Seifert fibering operators for 3D $\mathcal{N} = 2$ gauge theories, we formulate the necessary ingredients for a state-integral model of the topological quantum field theory dual to a given Seifert manifold under…
In this work we present a new approach to constructing Calabi-Yau orbifold models required for compactification in superstring theory. We use the connection of CY orbifolds with the class of exactly solvable N=2 SCFT models to explicitly…
In (equi-)affine differential geometry, the most important algebraic invariants are the affine (Blaschke) metric h, the affine shape operator S and the difference tensor K. A hypersurface is said to admit a pointwise symmetry if at every…
We construct explicit complex structures and transversely K\"ahler holomorphic foliations on $SU(3)$ corresponding to variations of real quadratic equations on a complex quadric in $\mathbb{C}^{6}$ as generalizations of left-invariant…
Using recent work of Bettiol, we show that a first-order conformal deformation of Wilking's metric of almost-positive sectional curvature on $S^2\times S^3$ yields a family of metrics with strictly positive average of sectional curvatures…
HyperK\"ahler spaces, including manifolds, orbifolds and conical singularities play an important role in superstring/$M$-theory and gauge theories as well as in differential and algebraic geometry. In this paper we provide hundreds of new…
We consider deformations of the scalar curvature of a partially integrable pseudohermitian manifold, in analogy with the work of Fischer and Marsden on Riemannian manifolds. In particular, we introduce and discuss $R$-singular spaces, give…
From a certain strongly equivariant bundle gerbe with connection and curving over a smooth manifold on which a Lie group acts, we construct under some conditions a bundle gerbe with connection and curving over the quotient space. In…