Colocality and twisted sums of Banach spaces

Using the relation between subspaces of Banach spaces and quotients of their duals, we introduce the concept of colocality to give a new method that guarantees the existence of nontrivial twisted sums in which finite quotients play a major role (Theorem 1.7). An interesting point is that no restrictions are imposed on the quotients, only on the various subspaces. New examples of nontrivial twisted sums are given.