Dorette Pronk

Orbifolds, sheaves and groupoids

We characterize orbifolds in terms of their sheaves, and show that orbifolds correspond exactly to a specific class of smooth groupoids. As an application, we construct fibered products of orbifolds and prove a change-of-base formula for sheaf cohomology. Mathematics Subject Classifications (1991): 22A22, 57S15, 55N30, 18B25.

Simplicial Cohomology of Orbifolds

Abstract For any orbifold M , we explicitly construct a simplicial complex S( M ) from a given triangulation of the ‘coarse’ underlying space together with the local isotropy groups of M . We prove that, for any local system on M , this complex S( M ) has the same cohomology as M . The use of S( M ) in explicit calculations is illustrated in the example of the ‘teardrop’ orbifold.

Model structures on the category of small double categories

In this paper we obtain several model structures on DblCat, the category of small double categories. Our model structures have three sources. We first transfer across a categorification-nerve adjunction. Secondly, we view double categories as internal categories in Cat and take as our weak equivalences various internal equivalences defined via Grothendieck topologies. Thirdly, DblCat inherits a model structure as a category of algebras over a 2‐monad. Some of these model structures coincide and the different points of view give us further results about cofibrant replacements and cofibrant objects. As part of this program we give explicit descriptions for and discuss properties of free double categories, quotient double categories, colimits of double categories, horizontal nerve and horizontal categorification. 18D05, 18G55; 55P99, 55U10

Erratum: Translation Groupoids and Orbifold Cohomology

We correct an error in the proof of a lemma in Translation Groupoids and Orbifold Cohomology, Canadian J. Math Vol 62 (3), pp 614-645 (2010). _is error was pointed out to the authors by Li Du of the Georg-August-Universität at Gottingen, who also suggested the outline for the corrected proof.