Twists over étale groupoids and twisted vector bundles

Fell Bundles over Groupoids

We study the C*-algebras associated to Fell bundles over groupoids and give a notion of equivalence for Fell bundles which guarantees that the associated C*-algebras are strong Morita equivalent. As a corollary we show that any saturated Fell bundle is equivalent to a semi-direct product arising from the action of the groupoid on a C*-bundle. A C*-algebraic bundle (see [F2, §11]) over a locally...

Twisted Vector Bundles on Pointed Nodal Curves

This paper grew out of an attempt to understand a recent draft of Seshadri ([Se2]) and is meant as a contribution in the quest for a good compactification of the moduli space (or stack) of G-bundles on a nodal curve. We are led by the idea that such a compactification should behave well in families and also under partial normalization of nodal curves. This statement may be reformulated by sayin...

Loop Groupoids and Twisted

The purpose of this paper is to introduce the notion of loop groupoid LG associated to a groupoid G. After studying the general properties of LG, we show how this notion provides a very natural geometric interpretation for the twisted sectors of an orbifold [7], and for the inner local systems introduced by Ruan [14] by means of a natural generalization of the concept holonomy of a gerbe.

Twisted Torus Bundles over Arithmetic Varieties

A twisted torus is a nilmanifold which is the quotient of a real Heisenberg group by a cocompact discrete subgroup. We construct fiber bundles over arithmetic varieties whose fibers are isomorphic to a twisted torus, and express the complex cohomology of such bundles over certain Riemann surfaces in terms of automorphic forms.

Vector bundles over algebraic curves