# 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 $H_\ast(\overline{\mathcal{M}})$.

- Mathematics
- 2020

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 higher… Expand

Massey Products for Graph Homology

- Mathematics
- 2019

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 homotopy… Expand

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