Abstract
We introduce the notions of linked space, linked quasi-category and linked manifold, which are certain spans of the ordinary versions of the respective objects, and which model stratified spaces of various kinds. We then transfer, in depth 1, certain phenomena and constructions from stratified topology to this setting, such as exit path quasi-categories and the beginnings of a stratified bundle theory. We then discuss and extend the topology underlying a construction of J. Lurie, which associates a functorial field theory to any framed disk algebra, to arbitrary tangential structure, as well as an incorporation of defects which is native to the linked setting.