Related papers: SU(3) structures on S2 bundles over four-manifolds

The potential global topological obstructions to the tetrad approach to finding the quasi-local conserved quantities, associated with closed, orientable spacelike 2-surfaces S, are investigated. First we show that the Lorentz frame bundle…

Let $(M,I,J,K)$ be a hyperkahler manifold, and $Z\subset (M,I)$ a complex subvariety in $(M,I)$. We say that $Z$ is trianalytic if it is complex analytic with respect to $J$ and $K$, and absolutely trianalytic if it is trianalytic with…

In this paper, we analyze the possible homotopy types of the total space of a principal $SU(2)$-bundle over a $3$-connected $8$-dimensional Poincar\'{e} duality complex. Along the way, we also classify the $3$-connected $11$-dimensional…

We study rank 3 stable bundles E on P^3 as extensions of a line bundle B on a smooth surface S in P^3 by the direct sum of three copies of O_{P^3}(-\nu). In most cases, S (the dependency locus of three sections of E(\nu)) lies in the…

We present a construction (and classification) of certain invariant 2-forms on the real symplectic group. They are used to define a symplectic form on the quotient by a maximal torus and to "lift" a symplectic structure from a symplectic…

For a Lie group G and a smooth manifold W, we study the difference between smooth actions of G on W and bundles over the classifying space of G with fiber W and structure group Diff(W). In particular, we exhibit smooth manifold bundles over…

The main aim of this paper is to construct a complex analytic family of symmetric projective K3 surfaces through a compactifiable deformation family of complete quasi-projective varieties from $\operatorname{CP}^2…

We study the $\rm{SU}(3)$-structure induced on an oriented hypersurface of a 7-dimensional manifold with a nearly parallel $\rm{G}_2$-structure. We call such $\rm{SU}(3)$-structures nearly half-flat. We characterise the left invariant…

We present SU$(2|1)$ supersymmetric mechanics on $n$-dimensional Riemannian manifolds within the Hamiltonian approach. The structure functions including prepotentials entering the supercharges and the Hamiltonian obey extended curved WDVV…

In this paper, complex vector bundles of rank $r$ over $8$-dimensional spin$^{c}$ manifolds are classified in terms of the Chern classes of the complex vector bundles and the cohomology ring of the manifolds, where $r = 3$ or $4$. As an…

We classify SO(n)-equivariant principal bundles over $S^n$ in terms of their isotropy representations over the north and south poles. This is an example of a general result classifying equivariant $(\Pi, G)$-bundles over cohomogeneity one…

Two hierarchies of quantum principal bundles over quantum real projective spaces are constructed. One hierarchy contains bundles with U(1) as a structure group, the other has the quantum group $SU_q(2)$ as a fibre. Both hierarchies are…

We describe a sufficient condition for actions constructed in projective superspace to possess an SU(2) R-symmetry. We check directly that this condition implies that the corresponding hyperkahler varieties, constructed by means of the…

We show that an oriented elliptic 3-manifold admits a universally tight positive contact structure iff the corresponding group of deck transformations on $S^3$ preserves a standard contact structure pointwise. We also relate univerally…

Let M be a closed 3-manifold and S(M) the skein module of M at some odd root of unity. Using the Frobenius morphism, we can see S(M) as the space of global sections of a coherent sheaf over the SL2 character scheme of M. We prove that when…

In this paper we describe how one can obtain Lie group structures on the group of (vertical) bundle automorphisms for a locally convex principal bundle P over the compact manifold M. This is done by first considering Lie group structures on…

We show how to use divisors on the projectivized Hodge bundle to construct special vector-valued modular forms and then apply invariant theory to construct all vector-valued Siegel modular forms of level two and degree two. Thus we…

A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly,…

We consider compact connected six dimensional symplectic manifolds with Hamiltonian SU(2) or SO(3) actions with cyclic principal stabilizers. We classify such manifolds up to equivariant symplectomorphisms.

We study moduli spaces of sheaves over non-projective K3 surfaces. More precisely, if $v=(r,\xi,a)$ is a Mukai vector on a K3 surface $S$ with $r$ prime to $\xi$ and $\omega$ is a "generic" K\"ahler class on $S$, we show that the moduli…