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

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

2008-02-25

arxiv.org/abs/0802.3675v3

Mathematics

Algebraic Geometry

Reference added for the formula in Prop. 11.6. Prop 11.7 corrected. Introduction changed accordingly

Scientific paper

We define an Artin stack which may be considered as a substitute for the non-existing (or empty) moduli space of stable two-pointed curves of genus zero. We show that this Artin stack can be viewed as the first term of a cyclic operad in the category of stacks. Applying the homology functor we obtain a linear cyclic operad. We formulate conjectures which assert that cohomology of a smooth projective variety has the structure of an algebra over this homology operad and that gravitational quantum cohomology can naturally expressed in terms of this algebra. As a test for these conjectures we show how certain well-known relations between gravitational correlators can be deduced from them.

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