Related papers: Complex structure on the six dimensional sphere fr…
Let $\bar{L}_i\lr X_i$ be a holomorphic line bundle over a compact complex manifold for $i=1,2$. Let $S_i$ denote the associated principal circle-bundle with respect to some hermitian inner product on $\bar{L}_i$. We construct complex…
Motivated by a recently identified severe discrepancy between a static and a dynamic theory of glasses, we numerically investigate the behavior of dense hard spheres in spatial dimensions 3 to 12. Our results are consistent with the static…
In this article, we review gauge-Higgs unification models based on gauge theories defined on six-dimensional spacetime with $S^2/Z_2$ topology in the extra spatial dimensions. On the extra $S^2/Z_2$ space, non-trivial boundary conditions…
Generically an almost complex structure has no symmetries at all, but there exist symmetric structures. In this paper we describe how to guarantee that the pseudogroup of local symmetries is small (finite-dimensional). It will be indicated…
In this work we deal with left invariant complex and symplectic structures on simply connected four dimensional solvable real Lie groups. We search the general form of such structures, when they exist and we make use of this information to…
The main purpose of this note is to construct almost complex or complex structures on certain isoparametric hypersurfaces in unit spheres. As a consequence, complex structures on $S^1\times S^7\times S^6$, and on $S^1\times S^3\times S^2$…
This paper aims to derive a definition of complexity for a dynamic spherical system in the background of self-interacting Brans-Dicke gravity. We measure complexity of the structure in terms of inhomogeneous energy density, anisotropic…
In this paper we show that the dimensionally reduced Seiberg-Witten equations lead to a Higgs field and study the resulting moduli spaces. The moduli space arising out of a subset of the equations, shown to be non-empty for a compact…
This article deals with 3-forms on 6-dimensional manifodls, the first dimension where the classification of 3-forms is not trivial. There are three classes of multisymplectic 3-forms there. We study the class which is closely related to…
We suggest that the electroweak Higgs particles can be identified with extra-dimensional components of the gauge fields, which after compactification on a certain topologically non-trivial background become tachyonic and condense. If the…
Self-duality is a very important concept in the study and applications of topological solitons in many areas of Physics. The rich mathematical structures underlying it lead, in many cases, to the development of exact and non-perturbative…
A four-dimensional analog of Chern-Simons theory produces integrable lattice models from Wilson lines and surface operators. We show that this theory describes a quasi-topological sector of maximally supersymmetric Yang-Mills theory in six…
Inspired by Coxeter's notion of Petrie polygon for $d$-polytopes (see \cite{Cox73}), we consider a generalization of the notion of zigzag circuits on complexes and compute the zigzag structure for several interesting families of…
We show that the process of spontaneous symmetry breaking can trap a field theoretic system in a highly non-trivial state containing a lattice of domain walls. In one large compact space dimension, a lattice is inevitably formed. In two…
Let A be a commutative ring, B a commutative A-algebra and M a complex of B-modules. We begin by constructing the square Sq_{B/A} M, which is also a complex of B-modules. The squaring operation is a quadratic functor, and its construction…
A method of constructing a class of bihamiltonian structures is presented. Elements of this class are generalizations of the so-called bihamiltonian structures of general position on odd-dimensional manifolds. The method consists in a…
The theory of $G$-structures provides us with a unified framework for a large class of geometric structures, including symplectic, complex and Riemannian structures, as well as foliations and many others. Surprisingly, contact geometry -…
A five dimensional $SU(6)$ grand gauge-Higgs unification compactified on $S^1/Z_2$ is discussed. We propose new sets of the $SU(6)$ representations where the quarks and leptons in one generation are embedded and there is no extra massless…
The coset spaces E$_8$/SO(10)$\times$H$_F$ allow complex structures which can account for three quark-lepton generations including right-handed neutrinos. We show that in the context of supersymmetric SO(10) gauge theories in 6 dimensions…
How is the universe organized on large scales? How did this structure evolve from the unknown initial conditions to the present time? The answers to these questions will shed light on the cosmology we live in, the amount, composition and…