Annellations

Annellations is a term found mainly in mathematical literature to describe either the formation or attachment of annuli—ring-shaped regions—in a space. An annulus is the region between two concentric circles (in the plane) or, more generally, a surface homeomorphic to S^1 × [0,1]. The word comes from annulus, Latin for ring, with the agent noun suffix -ation.

In one usage, annellation refers to creating an annulus inside a space by removing a disk; for example, removing an open disk from a surface yields a doubly connected region homeomorphic to an annulus.

Another usage describes attaching an annulus along its boundary to a space. This operation, common in low-dimensional topology, can change the boundary structure or connect boundary components by adding a cylindrical tube. Depending on the context, annellations may be described as annular attachments or as annulus-based cobordisms.

Because the term is uncommon and its precise meaning varies by author, definitions should be checked within its specific context. In practice, annellations are discussed mainly in relation to surface topology, geometric topology, and complex analysis when considering doubly connected regions or modular annuli in Riemann surfaces.

Related notions include the annulus itself, boundary components, and various forms of handle or tube attachments used in modifying surfaces.