High Quality Content by WIKIPEDIA articles! In mathematics, a filling of a manifold X is a cobordism W between X and the empty set. More to the point, the n-dimensional topological manifold X is the boundary of an n+1-dimensional manifold W. Perhaps the most active area of current research is when n = 3, where one may consider certain types of fillings.It is known that this list is strictly increasing in difficulty in the sense that there are examples of contact 3-manifolds with weak but no strong filling, and others that have strong but no Stein filling. Further, it can be shown that each type of filling is an example of the one preceding it, so that a Stein filling is a strong symplectic filling, for example. It used to be that one spoke of semi-fillings in this context, which means that X is one of possibly many boundary components of W, but it has been shown that any semi-filling can be modified to be a filling of the same type, of the same 3-manifold, in the symplectic world (Stein manifolds always have one boundary component).

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