cobordism

noun

1. (countable)A connection between two manifolds of the same dimension n via a manifold of dimension n+1, where the smaller manifolds are included in the boundary of the larger manifold.
2. (uncountable)The theory and study of such objects.

   “2008 April, John R. Harper, "Generalized cohomology, by Akira Kono and Dai Tamaki" (book review), Bulletin (New Series) of the American Mathematical Society volume 45 number 2, page 310, Cobordism revives the intuitive idea of bounding harbored in the original work of Poincaré but later sacrificed in order to construct a viable theory based on simpicial complexes.”