Related papers: Extensions of Instantons

We give a new method to construct linear spaces of matrices of constant rank, based on truncated graded cohomology modules of certain vector bundles as well as on the existence of graded Artinian modules with pure resolutions. Our method…

This paper establishes the projective equivalence between the Knizhnik-Zamolodchikov connection and the Hitchin connection in genus 0 with at least 3 marked points. The Knizhnik-Zamolodchikov connection is defined on the sheaf of conformal…

Associated to each finite dimensional linear representation of a group G, there is a vector bundle over the classifying space BG. This construction was studied extensively for compact groups by Atiyah and Segal. We introduce a homotopy…

We prove a general extension theorem for holomorphic line bundles on reduced complex spaces, equipped with singular hermitian metrics, whose curvature currents can be extended as positive, closed currents. The result has applications to…

We give a construction of $G_2$ and $Spin(7)$ instantons on exceptional holonomy manifolds constructed by Bryant and Salamon, by using an ansatz of spherical symmetry coming from the manifolds being the total spaces of rank-4 vector…

This thesis contains work which appeared in several papers. Additionally to the results in the papers it contains a detailed introduction and some further proofs and remarks. The dissertation gives a description of the topology and…

Let $\M_{k}^{n}$ be the moduli space of based (anti-self-dual) instantons on $\cpbar$ of charge $k$ and rank $n$. There is a natural inclusion of rank $n$ instantons into rank $n+1$. We show that the direct limit space is homotopy…

We construct a relative compactification of Dolbeault moduli spaces of Higgs bundles for reductive algebraic groups on families of projective manifolds that is compatible with the Hitchin morphism.

Special kinds of rank 2 vector bundles with (possibly irregular) connections on P^1 are considered. We construct an equivalence between the derived category of quasi-coherent sheaves on the moduli stack of such bundles and the derived…

We introduce a family of noncommutative 4-spheres, such that the instanton projector has its first Chern class trivial: $ch_1(e) = B \chi + b \xi$. We construct for them a 4-dimensional cycle and calculate explicitly the Chern-Connes paring…

We compare the invariants of flat vector bundles defined by Atiyah et al. and Jones et al. and prove that, up to weak homotopy, they induce the same map, denoted by $e$, from the $0$-connective algebraic $K$-theory space of the complex…

The aim of this paper is to give an explicit expression for Hitchin's connection in the case of rank 2 bundles with trivial determinant over curves of genus 2. We recall the definition of this connection (which arose in Quantum Field…

We interpret a class of 4k-dimensional instanton solutions found by Ward, Corrigan, Goddard and Kent as four-dimensional instantons at angles. The superposition of each pair of four-dimensional instantons is associated with four angles…

We study the equivalence among orientifold three-planes in the context of the Atiyah-Hirzebruch Spectral Sequence. This equivalence refers to the fact that two different cohomology classes in the same cohomology group, which classify the…

We study finite dimensional vector spaces over fields of elliptic functions equipped with two commuting aotomorphisms \sigma and \tau induced by isogenies of relatively prime orders. We give a structure theorem for such objects, that…

In this paper, it is proved that certain stable rank-3 vector bundles can be written as extensions of line bundles and stable rank-2 bundles. As an application, we show the rationality of certain moduli spaces of stable rank-3 bundles over…

We define four versions of equivariant instanton Floer homology ($I^+, I^-, I^\infty$ and $\widetilde I$) for a class of 3-manifolds and $SO(3)$-bundles over them including all rational homology spheres. These versions are analogous to the…

The total space of the spinor bundle on the four dimensional sphere S^4 is a quaternionic line bundle that admits a metric of Spin(7) holonomy. We consider octonionic Yang-Mills instanton on this eight dimensional gravitational instanton.…

Let $G$ be an infinite discrete group and let $\underline{E}G$ be a classifying space for proper actions of $G$. Every $G$-equivariant vector bundle over $\underline{E}G$ gives rise to a compatible collection of representations of the…

Throughout this paper, we comprehensively study instantons with every kind of continuous conformal symmetry. Examples of these objects are hard to come by due to non-linear constraints. However, by applying previous work on moduli spaces,…