bordant

Bordant is a term with several distinct meanings depending on the field. In topology, two closed n-dimensional manifolds M and N are bordant if there exists an oriented (n+1)-manifold W whose boundary is the disjoint union ∂W = M ⊔ (−N). Equivalently, M and N are the boundary of a single higher-dimensional manifold, up to orientation. This relation is an equivalence relation; its classes form the oriented bordism groups Ω_n. A basic example is that the n-sphere S^n is bordant to the empty set, since ∂D^{n+1} = S^n. Bordism theory, developed in the 20th century, provides algebraic invariants that distinguish manifolds and underpins the study of cobordism and characteristic classes.

In heraldry, bordant describes something that is bordered. It is used in blazonry to indicate that a charge or field carries a border or bordure, typically of a different tincture. The exact depiction depends on traditional blazon conventions, but the sense is that the edge of the object is outlined or surrounded by a border.

Etymology: bordant derives from Old French bordant, the present participle of border, from bord “edge, border.” In mathematics the usage is separate from the heraldic sense, though both share the same root word for “border.”

See also: Bordism, Cobordism, Blazonry.