Related papers: Monopole equations on 8-manifolds with Spin(7) hol…
We consider compactifications of M-theory on 7-manifolds in the presence of 4-form fluxes, which leave at least four supercharges unbroken. We focus especially on the case, where the 7-manifold supports two spinors which are SU(3) singlets…
Motivated by the cubic forms and anomaly cancellation formulas of Witten-Freed-Hopkins, we give some new cubic forms on spin, spin$^c$, spin$^{w_2}$ and orientable 12-manifolds respectively. We relate them to $\eta$-invariants when the…
Magnetic monopole solutions naturally arise in the context of spontaneously broken gauge theories. When the unbroken symmetry includes a non-Abelian subgroup, investigation of the low-energy monopole dynamics by means of the moduli space…
In this paper, we investigate the Seiberg-Witten gauge theory for Seifert fibered spaces. The monopoles over these three-manifolds, for a particular choice of metric and perturbation, are completely described. Gradient flow lines between…
Using gauge theory for Spin(7)-manifolds of dimension 8, we develop a procedure, called Spin-rotation, which transforms a (stable) holomorphic structure on a vector bundle over a complex torus of dimension 4 into a new holomorphic structure…
The principal theory of this paper comprises a technique for constructing associative, coassociative and Cayley submanifolds of Euclidean space with symmetries, using first-order ordinary differential equations. Explicit examples of…
We propose the Hamiltonian model of ${\cal N}=8$ supersymmetric mechanics on $n-$dimensional special K\"ahler manifolds (of the rigid type).
In this paper, we prove that the set of solutions of constraint equations for coupled Einstein and scalar fields in classical general relativity possesses Hilbert manifold structure. We follow the work of R. Bartnik [2] and use weighted…
We obtain all possible solutions of a 1/4 Bogomol'nyi-Prasad-Sommerfield equation exactly, containing configurations made of walls, vortices and monopoles in the Higgs phase. We use supersymmetric U(N_C) gauge theories with eight…
Spherical clusters of SU(2) BPS monopoles are investigated here. A large class of monopole solutions is found using an abelian approximation, where the clusters are spherically symmetric, although exact solutions cannot have this symmetry…
We re-investigate the construction of half-supersymmetric 7-brane solutions of IIB supergravity. Our method is based on the requirement of having globally well-defined Killing spinors and the inclusion of SL(2,Z)-invariant source terms. In…
The results of the paper concern the topological structure of complete riemannian manifolds with cyclic holonomy groups and low-dimensional orientable complete flat manifolds. We also discuss related results such as the affine…
In this paper, we study geometric rigidity of Riemannian manifolds admitting stable solutions of certain elliptic problems (stability in a variational sense), that is, under suitable hypotheses, we are able to characterize the Riemannian…
The monopole systems with hidden symmetry of the two-dimensional Coulomb problem are considered. One of them, the "charge-charged magnetic vortex" with a half-spin, is constructed by reducing the quantum circular oscillator with respect to…
In this paper we prove that a generic rational equation of degree $7$ is solvable by 2-fold origami. In particular we show how to septisect an arbitrary angle. This extends the work of Alperin & Lang and Nishimura on 2-fold origami.…
We investigate geometric properties of indecomposable but non-irreducible Lorentzian manifolds, which are total spaces of circle bundles. We investigate under which conditions these manifolds are complete and give examples which fulfill the…
For a compact spinc manifold $X$ with boundary $b_1(\partial X)=0$, we consider moduli spaces of solutions to the Seiberg-Witten equations in a generalized double Coulomb slice in $L^2_1$ (i.e., $W^{1,2}$) Sobolev regularity. We prove they…
The aim of the present paper is the investigation of $Spin(9)$-structures on 16-dimensional manifolds from the point of view of topology as well as holonomy theory. First we construct several examples. Then we study the necessary…
We prove that the moduli space of solutions to the PU(2) monopole equations is a smooth manifold of the expected dimension for simple, generic parameters such as (and including) the Riemannian metric on the given four-manifold. In a…
In studying the "11/8-Conjecture" on the Geography Problem in 4-dimensional topology, Furuta proposed a question on the existence of Pin(2)-equivariant stable maps between certain representation spheres. In this paper, we present a complete…