L3

  In this talk I will show how one can sometimes "uncomplete" the p-completed classifying space of a finite group, to obtain the original (non-completed) classifying space, and hence the original finite group. This "uncompletion" process is closely related to well-known local-to-global questions in group theory, such as the classification of finite simple groups. The approach goes via the theory of p-local finite groups. This talk is a report on joint work with Bob Oliver.