  We argue that any proposed quantum theory of gravity with non-trivial
cobordism classes in the space of configurations belongs to the Swampland. The
argument is based on the assumption that there are no global symmetries in a
consistent theory of quantum gravity. The triviality of the cobordism classes
requires the existence of certain stringy defects that trivialize the potential
cobordism classes. We provide evidence for this conjecture by identifying those
defects demanded by this argument that could preserve supersymmetry, and
predict the existence of new non-supersymmetric defects in string theory.
