Endotrivial representations of finite groups and equivariant line bundles on the Brown complex

Equivariant Bundles and Isotropy Representations

We introduce a new construction, the isotropy groupoid, to organize the orbit data for split Γ-spaces. We show that equivariant principal G-bundles over split Γ-CW complexes X can be effectively classified by means of representations of their isotropy groupoids. For instance, if the quotient complex A = Γ\X is a graph, with all edge stabilizers toral subgroups of Γ, we obtain a purely combinato...

The Equivariant Brauer Groups of Principal Bundles

Cohomology Groups of Deformations of Line Bundles on Complex Tori

The cohomology groups of line bundles over complex tori (or abelian varieties) are classically studied invariants of these spaces. In this article, we compute the cohomology groups of line bundles over various holomorphic, non-commutative deformations of complex tori. Our analysis interpolates between two extreme cases. The first case is a calculation of the space of (cohomological) theta funct...

Groups of Complex Line Bundles Over Compact Kähler Varieties.

Representations of Orbifold Groups and Parabolic Bundles