Corpus ID: 219179639

# Deformation theory of Cohomological Field Theories

@article{Dotsenko2020DeformationTO,
title={Deformation theory of Cohomological Field Theories},
author={V. Dotsenko and S. Shadrin and A. Vaintrob and B. Vallette},
journal={arXiv: Algebraic Geometry},
year={2020}
}
We develop the deformation theory of cohomological field theories (CohFTs), which is done as a special case of a general deformation theory of morphisms of modular operads. This leads us to introduce two new natural extensions of the notion of a CohFT: homotopical (necessary to structure chain-level Gromov--Witten invariants) and quantum (with examples found in the works of Buryak--Rossi on integrable systems). We introduce a new version of Kontsevich's graph complex, enriched with tautological… Expand
2 Citations
Toward a minimal model for $H_\ast(\overline{\mathcal{M}})$.
The modular operad $H_\ast(\overline{\mathcal{M}}_{g,n})$ of the homology of Deligne-Mumford compactifications of moduli spaces of pointed Riemann surfaces has a minimal model governed by higherExpand
Massey Products for Graph Homology
This paper shows that the operad encoding modular operads is Koszul. Using this result we construct higher composition operations on (hairy) graph homology which characterize its rational homotopyExpand

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