2008/02/25 by Ivan Kausz, Kausz, Ivan
Mathematics · #14H15 #14N35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14H15 #msc:14N35
paper · pdf · doi:10.48550/arxiv.0802.3675
Reference added for the formula in Prop. 11.6. Prop 11.7 corrected. Introduction changed accordingly
openalex publication_date 2008/02/25 · arxiv created 2008/02/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.