Related papers: A new approach to mod 2 decompositions of BSU(2) a…

We study holonomy groups coming from F-theory compactifications. We focus mainly on SO(8) as 12-4=8 and subgroups SU(4), Spin(7), G2 and SU(3) suitable for descent from F-theory, M-theory and Superstring theories. We consider the relation…

Let $Y$ be a pointed space and let $\mathcal E(Y^r)$ be the group of based self-equivalences of $Y^r$, $r\geq 2$. For $Y$ a homotopy commutative $H$-group we construct a subgroup $\mathcal E_{\mathrm{Mat}}(Y^r)$ of $\mathcal E(Y^r)$ which…

We study compactifications of type II theories on SU(2) x SU(2) structure manifolds to six, five and four spacetime dimensions. We use the framework of generalized geometry to describe the NS-NS sector of such compactifications and derive…

We classify all compact simply connected biquotients of the form $G/\!\!/ SU(2)^2$ for $G =SU(4), SO(7), Spin(7)$, or $G = \mathbf{G}_2\times SU(2)$. In particular, we show there are precisely $2$ inhomogeneous reduced biquotients in the…

The correlation between $B(E2)$ structure and triaxial deformation has been investigated within the framework of the proton-neutron boson model. The analysis reveals that the distinctive feature, characterized by…

We prove that any connected 2-compact group is classified by its 2-adic root datum, and in particular the exotic 2-compact group DI(4), constructed by Dwyer-Wilkerson, is the only simple 2-compact group not arising as the 2-completion of a…

For each of the groups $G = O(2), SU(2), U(2)$, we compute the integral and $\mathbb{F}_2$-cohomology rings of $B_\text{com} G$ (the classifying space for commutativity of $G$), the action of the Steenrod algebra on the mod 2 cohomology,…

A mapping class group of an oriented manifold is a quotient of its diffeomorphism group by the isotopies. We compute a mapping class group of a hypekahler manifold $M$, showing that it is commensurable to an arithmetic subgroup in SO(3,…

The fundamental bigroupoid of a topological space is one way of capturing its homotopy 2-type. When the space is semilocally 2-connected, one can lift the construction to a bigroupoid internal to the category of topological spaces, as Brown…

Eleven different types of "maximally superintegrable" Hamiltonian systems on the real hyperboloid $(s^0)^2-(s^1)^2+(s^2)^2-(s^3)^2=1$ are obtained. All of them correspond to a free Hamiltonian system on the homogeneous space…

We consider $SU(3)_{C}\times SU(2)_{AL}\times SU(2)_{BL}\times U(1)_{Y}$ as the low-energy subgroup of supersymmetric $SU(3)^{6}$ unification. This may imply small deviations from quark-lepton universality at the TeV scale, as allowed by…

Let Y = Hom(Z^n, SU(2)) denote the space of commuting n-tuples in SU(2). We determine the homotopy type of the suspension of Y and compute the integral cohomology groups of Y for all positive integers n.

The widths of a class of two-body $\bar{B}_s^0 $ decays induced by $b \to c \bar u d$ and $b \to c \bar u s$ transitions are determined in a model-independent way, using $SU(3)_F$ symmetry and existing information on $\bar B \to D_{(s)} P$…

We compute the fundamental group of the spaces of ordered commuting $n$-tuples of elements in the Lie groups SU(2), U(2) and SO(3). For SO(3) the computation of the mod-2 cohomology of the components of these spaces is also obtained.

We give a rather general construction of double categories and so, under further conditions, double groupoids, from a structure we call a `double module'. We also give a homotopical construction of a double groupoid from a triad consisting…

We first formulate a general scheme for the classification of 2-compact groups in terms of maximal torus normalizer pairs. Applying this scheme, we show that all connected and some non-connected 2-compact groups are N-determined. We also…

We record various properties of twisted Becker-Gottlieb transfer maps and study their multiplicative properties analogous to Becker-Gottlieb transfer. We show these twisted transfer maps factorise through Becker-Schultz-Mann-Miller-Miller…

We propose a simple, testable, SU(5) model within the context of the type II neutrino see-saw mechanism. It is based on requiring renormalizability, the absence of any other matter fields besides those already present in the Standard Model…

We deal with the symmetries of a (2-term) graded vector space or bundle. Our first theorem shows that they define a (strict) Lie 2-groupoid in a natural way. Our second theorem explores the construction of nerves for Lie 2-categories,…

In this tutorial, exponentiation and factorization (decomposition) formulas are derived and discussed for common matrix operators that arise in studies of classical dynamics, linear and nonlinear optics, and special relativity. To…