18 documents found, page 1 of 2

The Conformal Limit and Projective Structures

The non-abelian Hodge correspondence maps a polystable $\textrm{SL}(2, {\mathbb{R}})$-Higgs bundle on a compact Riemann surface $X$ of genus $g \geq 2$ to a connection that, in some cases, is the holonomy of a branched hyperbolic structure. Gaiotto's conformal limit maps the same bundle to a partial oper, that is, to a connection whose holonomy is that of a branched complex projective structure compatible with ...

Narasimhan-Ramanan branes and wobbly Higgs bundles

Narasimhan-Ramanan branes, introduced by the authors in a previous paper, consist of a family of BBB-branes inside the moduli space of Higgs bundles, and a family of complex Lagrangian subvarieties. It was conjectured that these complex Lagrangian subvarieties support the BBB-branes that are mirror dual to the Narasimhan-Ramanan BBB-branes. In this paper, we show that the support of these branes intersects nont...

Non-connected Lie groups, twisted equivariant bundles and coverings

Let gamma be a finite group acting on a Lie group G. We consider a class of group extensions 1 -> G -> G -> gamma -> 1 defined by this action and a 2-cocycle of gamma with values in the centre of G. We establish and study a correspondence between G-bundles on a manifold and twisted gamma-equivariant bundles with structure group G on a suitable Galois gamma-covering of the manifold. We also describe this corresp...

Stratifications on the nilpotent cone of the moduli space of Hitchin pairs

We consider the problem of finding the limit at infinity (corresponding to the downward Morse flow) of a Higgs bundle in the nilpotent cone under the natural C*-action on the moduli space. For general rank we provide an answer for Higgs bundles with regular nilpotent Higgs field, while in rank three we give the complete answer. Our results show that the limit can be described in terms of data defined by the Hig...

On the classification of the rigid motions of the plane

On Eulers Rotation Theorem

Summary: It is well known that a rigid motion of the Euclidean plane can be written as the composition of at most three reflections. It is perhaps not so widely known that a rigid motion of n-dimensional Euclidean space can be written as the composition of at most n + 1 reflections. The purpose of the present article is, firstly, to present a natural proof of this result in dimension 3 by explicitly constructin...

Unramified covers and branes on the Hitchin system

We study the locus of the moduli space of GL(n, C)-Higgs bundles on a curve given by those Higgs bundles obtained by pushforward under a connected unramified cover. We equip these loci with a hyperholomorphic bundle so that they can be viewed as BBB-branes, and we introduce corresponding BAA-branes which can be described via Hecke modifications. We then show how these branes are naturally dual via explicit Four...

SO(p,q)-Higgs bundles and Higher Teichmuller components

Some connected components of a moduli space are mundane in the sense that they are distinguished only by obvious topological invariants or have no special characteristics. Others are more alluring and unusual either because they are not detected by primary invariants, or because they have special geometric significance, or both. In this paper we describe new examples of such 'exotic' components in moduli spaces...

Quiver bundles and wall crossing for chains

Holomorphic chains on a Riemann surface arise naturally as fixed points of the natural C-action on the moduli space of Higgs bundles. In this paper we associate a new quiver bundle to the Hom-complex of two chains, and prove that stability of the chains implies stability of this new quiver bundle. Our approach uses the Hitchin-Kobayashi correspondence for quiver bundles. Moreover, we use our result to give a ne...

Homotopy type of moduli spaces of G-Higgs bundles and reducibility of the nilpo...

Let G be a real reductive Lie group, and H-C the complexification of its maximal compact subgroup H subset of G. We consider classes of semistable G-Higgs bundles over a Riemann surface X of genus g >= 2 whose underlying H-C-principal bundle is unstable. This allows us to find obstructions to a deformation retract from the moduli space of G-Higgs bundles over X to the moduli space of H-C-bundles over X, in cont...