  We propose an alternative representation for linear quantum gravity. It is
based on the use of a structure that bears some resemblance to the Abelian loop
representation used in electromagnetism but with the difference that space of
extended object on which waves functions take values have a structure of
commutative monoid instead of Abelian group. The generator of duality of the
theory is realized in this representation and a geometrical interpretation is
discussed.
