The operation of gluing two manifolds with the "same" boundary
together to get a closed manifold extends sequilinearly to pairings on
universal spaces. In low dimensions these pairing seem to have a
positivity property but in higher dimensions null vectors appear. This
phenomena tells us something about possible generalizations of Chern
-Simons theory and suggests a novel reason that the connection between
quantum mechanics and topology may be strongest in two spatial
dimensions.