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A set of physical operators which are responsible for touching interactions in the framework of c<1 unitary conformal matter coupled to 2D quantum gravity is found. As a special case the non-critical bosonic strings are considered. Some analogies with four dimensional quantum gravity are also discussed, e.g. creation-annihilation operators for baby universes, Coleman mechanism for the cosmological constant.doi:10.1103/physrevd.57.3725 fatcat:dz5wze4pgvedzgb4bgyf4gjngy