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We define an Artin stack which may be considered as a substitute for thenon-existing (or empty) moduli space of stable two-pointed curves of genuszero. We show that this Artin stack can be viewed as the first term of a cyclicoperad in the category of stacks. Applying the homology functor we obtain alinear cyclic operad. We formulate conjectures which assert that cohomology ofa smooth projective variety has the structure of an algebra over this homologyoperad and that gravitational quantum cohomology can naturally expressed interms of this algebra. As a test for these conjectures we show how certainwell-known relations between gravitational correlators can be deduced fromthem.

A Cyclic Operad in the Category of Artin Stacks and Gravitational Correlators