The White Rose Consortium ePrints Repository: creating a shared institutional repository for the Universities of Leeds, Sheffield and York

The White Rose Consortium ePrints Repository was created as part of the JISC funded SHERPA project . The Consortium is a partnership between the Universities of Leeds, Sheffield and York. The three universities share a single installation of the open source EPrints software (developed by Southampton University). The repository houses published research output from across the consortium – primarily peer-reviewed journal papers – and can be viewed at http://eprints.whiterose.ac.uk/. Currently, all the repository content is openly accessible and our access statistics suggest a good level of usage, with many users coming into the system through Google and other search engines

Hyperplane arrangements and K-theory

We study the Z/2-equivariant K-theory of the complement of the complexification of a real hyperplane arrangement. We compute the rational K and KO rings, and give two different combinatorial descriptions of the subring of the integral KO ring generated by line bundles.Comment: 11 pages, no figures; final version, to appear in Topology and its Application

Moduli spaces for Bondal quivers

Given a sufficiently nice collection of sheaves on an algebraic variety V, Bondal explained how to build a quiver Q along with an ideal of relations in the path algebra of Q such that the derived category of representations of Q subject to these relations is equivalent to the derived category of coherent sheaves on V. We consider the case in which these sheaves are all locally free and study the moduli spaces of semistable representations of our quiver with relations for various stability conditions. We show that V can often be recovered as a connected component of such a moduli space and we describe the line bundle induced by a GIT construction of the moduli space in terms of the input data. In certain special cases, we interpret our results in the language of topological string theory.Comment: 17 pages, major revisio

Abelianization for hyperkahler quotients

We study an integration theory in circle equivariant cohomology in order to prove a theorem relating the cohomology ring of a hyperkahler quotient to the cohomology ring of the quotient by a maximal abelian subgroup, analogous to a theorem of Martin for symplectic quotients. We discuss applications of this theorem to quiver varieties, and compute as an example the ordinary and equivariant cohomology rings of a hyperpolygon space.Comment: 18 pages, 1 figur