Classification of extensions of principal bundles and transitive Lie groupoids with prescribed kernel and cokernel

The equivalence of principal bundles with transitive Lie groupoids due to Ehresmann is a well known result. A remarkable generalisation of this equivalence, due to Mackenzie, is the equivalence of principal bundle extensions with those transitive Lie groupoids over the total space of a principal bundle, which also admit an action of the structure group by automorphisms. This paper proves the existence of suitably equivariant transition functions for such groupoids, generalising consequently the classification of principal bundles by means of their transition functions, to extensions of principal bundles by an equivariant form of \v{C}ech cohomology.Comment: 23 page

Exploring the feasibility of international collaboration and relationship building through a virtual partnership scheme

International collaboration is an under-studied component of the Scholarship of Teaching and Learning (SoTL). This study sheds light on the process of international collaboration by illustrating an exploratory approach to the process of forming and maintaining collaborative partnerships. Participants in this study were put into pairs (each one comprised of one individual from the University of Glasgow and another from the University of Wisconsin System) and asked to participate in email correspondence over the course of one year. The text of participants’ emails was pooled and analyzed through a general inductive approach using NVivo software. The study, though small in nature, helps to illustrate and further understand international collaborative relationships. We offer suggestions for future international collaborations and discuss the implications of emphasizing such partnerships within SoTL